TEHRAN—Decorated with a foosball table, brightly colored walls and videogame consoles, the offices of Café Bazaar look no different than many Internet startups in technology hubs like San Francisco, London or Berlin.

What’s unique about Café Bazaar, an Android software app store that mimics Google Inc.’s Google Play, is its location: an upscale high rise in central Tehran.

The company is among dozens that have popped up in Iran, part of a technology scene that has developed amid—and some say because of—international sanctions and strict censorship laws that have scared off global tech companies, at least for now.

Facebook and Twitter, whose users include the offices of Ayatollah Ali Khamenei and President Hassan Rouhani, are particularly popular with Iran’s increasing tech-savvy population of 78 million people. But foreign companies, deterred by international sanctions or banned in Iran, have yet to launch Iranian versions of their content.

But those hurdles are fueling the rise of fast-growing local companies. Café Bazaar offers more 25,000 downloadable Iranian and international apps for gaming, social media, messaging and other uses, and it gets roughly 20 million visits a week within Iran.