Magnolia Bakery, the New York City purveyor of cupcakes once prized by the gals on “Sex in the City”—and featured in the “Saturday Night Live” video “Lazy Sunday”—received state approval this week to sell franchises and is eyeing overseas markets as diverse as Sao Paulo, Tokyo and Doha, Qatar.

The new franchises will only be sold abroad, according to the store’s co-owner, Steve Abrams. He says the bakery’s vintage cakes and desserts are already popular outside the U.S., thanks in no small part to Carrie Bradshaw, the sex columnist portrayed by Sarah Jessica Parker on the widely syndicated HBO series.

“The show resonated with people all over the world and that’s been great for us,” says Mr. Abrams, who adds he has been approached by thousands of budding franchisees over the years, ranging from mom-and-pop tourists to chief executives of multinational corporations.

The bakery has also made appearances in “The Devil Wears Prada,” “Spin City,” “Late Night with Conan O’Brien” and “Veronica Mars.”

Mr. Abrams says the bakery is largely perceived as a luxury brand outside the U.S., especially in emerging markets in South America and the Middle and Far East that now have a growing appetite for high-end western luxury goods. The company is courting prospective buyers in Hong Kong, India, Qatar, Kuwait and Brazil, among other places, he says.

“The time is right,” he says.

Meanwhile Abrams, along with his wife, Tyra, will continue to oversee the four New York locations and an outlet in Los Angeles. A location is currently being planned in Chicago, as well as in Bloomingdale’s flagship store in Manhattan. All of the U.S. locations will be owned by Magnolia Operating LLC, the Abrams’ New York-based company. An online store is also in the works, which will offer nationwide delivery.

Mr. Abrams says they’ve developed manuals, recipe books and other training materials to ensure the international outlets offer as close to the same experience as possible—though he also anticipates some regional variations, such as a green tea cupcake at stores in Japan.

The original Greenwich Village store opened in 1996. Owners Allysa Torey and Jennifer Appel started out with just a handful of employees, offering fresh bread and cinnamon rolls. They soon added vanilla cake with pink-tinted buttercream-icing cupcakes, sparking a craze among the neighborhood’s late-night crowd. Four years later, Ms. Appel left to start her own bakery, and in 2007 Ms. Torey sold the store to the Abrams.

Today, cupcakes make up just 50% of the company’s business, Mr. Abrams says. The bakeries now produce some 60 different products with 120 variations, inlcuding cakes and pies, banana pudding, cookies, mini-cheesecakes and breakfast muffins.

“We’re a lot more than just cupcakes,” Mr. Abrams says.