From Arab Fashion Week, based in Dubai, United Arab Emirates, which debuted last month on the heels of Paris Fashion Week, to Jakarta Fashion Week, held last week in the Indonesian capital, formal fashion showcases are being institutionalized across the Islamic world.

At the same time, private individuals are also claiming their due. A 15-year-old Saudi teenager called for the development of a hijab-clad emoji this fall, while a fully clothed Muslim journalist was featured wearing a hijab in the October edition of Playboy. If fashion helps define a social and cultural narrative, then this movement is focused on reshaping the perception of 21st-century Muslim female identity in ways that go far beyond the veil.

“This Vogue is very overdue,” said Deena Aljuhani Abdulaziz, 41, the Riyadh-based Saudi princess, former retailer and newly crowned editor in chief of Vogue Arabia, while she was in Paris during fashion week last month. “The Arabs deserve their Vogue, and they’ve deserved it for a long, long time.”

Though Vogue Arabia is not the first foreign women’s lifestyle magazine to publish an offshoot in the Gulf (Harper’s Bazaar, Marie Claire and Elle all publish Arabian editions, for example), its audience ambitions extend far beyond its immediate geographical borders.

“The Vogue Arabia woman is one who celebrates her tradition but also considers herself a highly educated global citizen,” Ms. Aljuhani Abdulaziz said. “Don’t forget that we understand luxury almost better than anyone else on earth. Middle Eastern women have been serious couture clients since the late 1960s. We’ve been around long before the Russians and the Chinese ever came into the picture.”

A key part of her Vogue editorial mission, she said, is to eradicate misconceptions around the Arab and Muslim diaspora. The new magazine’s headquarters will be in Dubai, and alongside the online platform starting next March, the 25-member editorial team will produce 11 print issues a year, two of which will be solely in Arabic.

“Vogue Arabia is not just about appealing to our own region, but about providing a cross-cultural bridge, a beautiful source of inspiration you would want to pick up even if you were from another area,” she said.

“Many people don’t really know exactly what Arabia is, and there are major misunderstandings around modest dressing, too,” Ms. Aljuhani Abdulaziz added. “I have a responsibility to tackle those issues, through a fashion lens, of course. I am not interested in being a political magazine. There are plenty of others who do that. But what I can lay out to readers, both near and far, is that what brings us together is far greater than what sets us apart.”

Anniesa Hasibuan, 30, would agree. The Indonesian designer of modest fashion collections with 124,000 followers on Instagram made history in September during New York Fashion Week with a catwalk show in which every model wore hijabs in ivory, peach and gray silk.

A hijab is not just a symbol or a statement, “but a part of a Muslim woman’s identity, an identity they are asserting more confidently,” Ms. Hasibuan said. (Her show received a standing ovation.) “I believe fashion is one of the outlets in which we can start that cultural shift in today’s society to normalize the hijab in America and other parts of the West, so as to break down stereotypes and demystify misconceptions.”

Indeed, modest fashion is fast becoming a commercial phenomenon; the global Muslim clothing market is forecast to be worth $327 billion by 2020, according to the latest Global Islamic Economy report — larger than the current clothing markets of Britain ($107 billion), Germany ($99 billion) and India ($96 billion) combined. And a rising Muslim middle class, having greater affluence and sophisticated tastes as well as pride in its religion, is likely to triple from an estimated 300 million in 2015 to 900 million by 2030, according to Ogilvy Noor, the Islamic branding consultancy.

So it is of no surprise that in the last 18 months, a host of Western brandshave made their own efforts to get into this booming market, like DKNY, which created a Ramadan capsule collection in 2014; to Tommy Hilfiger; and Dolce & Gabbana, which included a range of luxury hijabs and abayas, made from the same fabrics as the rest of its collection. Not to mention Marks & Spencer’s controversial burkini, and Uniqlo’s LifeWear collection, created in collaboration with a Muslim fashion designer, Hana Tajima, which includes “breezy dresses” and “iconic hijabs.”

Shelina Janmohamed, vice president of Ogilvy Noor, said: “The rise in modest fashion over the last decade has come hand in hand with the emergence of ‘Generation M’: Muslims who believe that faith and modernity go hand in hand. They want to wear their religion with pride but also feel part of the societies around them.”

She said that more than one-third of today’s Muslims are younger than 15, and nearly two-thirds are younger than 30. And when it comes to young women, more are digitally connected, marrying later and in possession of a disposable income than ever before.

“Consumption is part of their identity,” Ms. Janmohamed said. “When they buy products that help them better their practice and that reinforce their beliefs, then they believe it will also make them better Muslims.”

Events like the Muslim Lifestyle Expo, held last weekend in Manchester, England, and now in its second year, offer smaller Muslim lifestyle brands the platform to showcase their products and services in the realms of halal food and travel, finance and fashion, to over 10,000 attendees.

The modest fashion catwalk, which hosts three to four runway shows per day, largely from foreign brands, is the centerpiece of the weekend, said the Expo’s chief executive, Tahir Mirza, though it also includes live cooking demonstrations and workshops on Islamic art put on by local galleries.

“The shows are packed,” Mr. Mirza said. “Many young British Muslim women love these modest fashion houses from abroad, because they have westernized branding but traditional values. And they don’t want to compromise.”

For Jacob Abrian, the chief executive of the Arab Fashion Council, the industry body responsible for organizing Arab Fashion Week, his primary focus beyond show seasons is on reinforcing local infrastructure and the framework necessary to create a viable, interconnected fashion industry across the region. By strengthening the existing manufacturing roots and luxury heritage — from the small traditional factories and village damask weavers to glossy fashion houses being started from the glittering skyscrapers of the Gulf — and encouraging Western designers to come and showcase their work to a valuable client base, the Middle East could become a center for fashion in its own right.

Ms. Aljuhani Abdulaziz appeared acutely aware that her role as Vogue Arabia editor in chief would require relentless careful navigation of religious and regional codes.

But as the first Vogue editor to have formerly been a retailer (she was a founder of a fashion concept store in Riyadh called D’NA), she pointed out that she was in the best possible position to understand the demands of her 21st-century readership, “be it the sophisticated Qatari woman able to shop in Europe, or to help a young woman in a remote village in Algeria or Yemen have dreams and feel like she can belong to something.”

“This job is not without its challenges,” she said. “It only really dawned on me after the appointment that this won’t just be me doing something I love, but is also a massive responsibility. But I know what offends in this world and what doesn’t, because I am one of them. I have my own sensitivities as to what is appropriate and what is not. I certainly don’t believe that you have to have blatant sexuality or absolute nudity to do a beautiful editorial.”

As the furor set off by France’s attempt to bar Muslim women wearing burkinis in public this summer proved, tensions around the right to bare skin (or not) and what freedom really looks like still simmer across the world. Reina Lewis, a professor of cultural studies at London College of Fashion, UAL, and the author of “Muslim Fashion: Contemporary Style Cultures,” suggested that Vogue Arabia may struggle to be all things to all people.

“Any regional title outside the so-called Western world has to make decisions on models and their ethnicity, skin color and body type rather than the usual default Caucasian, and consider considering cultural distinctions,” Ms. Lewis said. “But Vogue Arabia will have to constantly cross overtly into religious as well as national and regional identities, practices and a variety of income brackets in order to find her reader. And that won’t always be easy.

“Then again,” she continued, “this is something Western brands are being forced to think about more and more when it comes to appealing to observant women from numerous religious backgrounds. Fashion designers in particular need to think more laterally about how they design and the nonnegotiable elements of some lifestyles they design for.

“Modest fashion and Muslim fashion are no longer on the periphery of the industry, and an industry that stopped being able to afford to be elitist and exclusive long ago. This movement is really driven by an empowered new demographic who are expressing their presence in the modern world, and attempting to assert their place in it.”