President Blaise Compaore is apparently not in the presidential compound. Agence France Presse reported that Compaore has fled the capital to his hometown of Ziniare.
It was not clear if there were casualties.
About two hours after the shooting began, gunfire was also heard near the state radio station in Ouagadougou, the capital. There were no casualties.
Compaore seized power in a bloody coup 23 years ago and was re-elected by a landslide in a November vote. Burkina Faso has been hit by unrest recently, with protests over rising prices of basic foods and mistreatment of prisoners.
Burkina Faso, which has high rates of unemployment and illiteracy, is ranked 161 out of 169 nations on the United Nation's Human Development Index.