Mike Shattuck, president of the Atlanta-based company, Focus Brands International, tells CNN there are plans to open Cinnabon outlets in Algeria, Tunisia and Morocco as well.
Shattuck said the 7,500-square-foot Cinnabon store is the first of 10 planned locations set to open in Libya over the next four years.
"Ultimately, we think there's an even larger opportunity in the country for us," Shattuck said.
Interestingly, the company had already been in negotiations with Libya for two years before the Moammar Gadhafi regime fell to revolutionary forces earlier this year.
"We quickly halted everything because the revolution happened," said Shattuck. "Fortunately we were able to secure the location, and it made it without serious damage."
And it seems the U.S. franchise is already a hit in Libya, registering more than $45,000 in sales during its first week.
"This is one of the questions I get asked most," Chuck Dittrich, executive director of the U.S.-Libya Business Association, told CNN. "When are American franchises coming to Libya?"