Soldiers and military vehicles took to the deserted streets of Ouagadougou after dawn on Friday, cutting off access to administrative buildings.
By mid-morning, the city, usually buzzing with motorbikes and cars, was quiet.
Schools, businesses and banks were shut, state television stopped broadcasting.
It was not clear if the gunfire near a military base and the explosion was part of a coup attempt, but security sources say there had been frustration within the military at a lack of progress in combating Islamist militants.
Damiba, who took power in a coup in January, urged calm in a statement.
Certain members of the armed forces overcome by “moods swings’’ had created a “confused situation,’’ he said.
His whereabouts were unknown.
The latest unrest bore the hallmarks of other power grabs that had swept across West and Central Africa over the past two years, undoing years of democratic progress.
The coups had been driven in part by violence committed by Islamist groups who had taken over large areas of northern Burkina Faso and parts of neighbouring Mali and Niger.
Civilian populations had cheered military juntas in the hope that they would be more successful at containing the insurgents than their democratically-elected predecessors.