There was no immediate claim of responsibility for the violence, which continued early Monday and brought back painful memories of a January 2016 attack at a cafe that left 30 people dead.
At least four people had been killed and 11 others were wounded, according to an official at the Yalgado Hospital in Ouagadougou. The employee spoke on condition of anonymity as they were not authorized to speak to journalists.
Security forces arrived at the scene with armored vehicles after reports of shots fired near an upscale restaurant in Ouagadougou.
Police spokesman Capt. Guy Ye told The Associated Press the target of the attack was a Turkish restaurant known as Aziz Istanbul.
Burkina Faso, a landlocked nation in West Africa, is one of the poorest countries in the world. It shares a northern border with Mali, which has long battled Islamic extremists.
The three attackers in the 2016 massacre were of foreign origin, according to al-Qaida in the Islamic Maghreb, which claimed responsibility in the aftermath along with the jihadist group known as Al Mourabitoun. But the terror threat in
Burkina Faso is increasingly homegrown, experts say.
The northern border region is now the home of a local preacher, Ibrahim Malam Dicko, who radicalized and has claimed recent deadly attacks against troops and civilians. His association, Ansarul Islam, is now considered a terrorist group by Burkina Faso's government.