One gendarme was killed in the fighting in the Rayongo neighbourhood, while five people, including one civilian, were injured, the Minister of Security, Clement Sawadogo, said.
Ouagadougou has been hit by several Islamist militant attacks in recent years.
In March, militants from a Mali-based al Qaeda affiliate killed eight people and wounded dozens more in coordinated raids on the army headquarters and French embassy.
Burkinabe soldiers and police have also come under repeated attack near the borders with Mali and Niger, where militant groups linked to al Qaeda and Islamic State easily cross the porous frontiers.
“I think there is no point in calling them ‘suspected’ terrorists since they had a arsenal for combat which they used to respond to our men. So this is proof, clear and simple, that they were terrorists, equipped to carry out missions. A fourth one was captured who was near the toilet and this latter one will be used (part of) in the investigation. Unfortunately in this operation, a high risk operation, we lost one of our valiant men who died of his injuries and four others were injured and are now in hospital. Two civilians were also injured,” Burkina Faso minister of security, Clement Sawadogo informed.