Police were investigating Sunday's shooting, Col. Pierre-Claver Gahungu said.
The mayor of Bujumbura's northern district said police shot blindly into the crowd after the group started setting off fireworks.
"People were celebrating Italy's victory, firing fireworks in the street," Cibitoke Mayor Eric Masumbuko told The Associated Press. "Policemen first launched a grenade in the group and then started firing guns on them."
Two people died at the scene and another died Monday morning, he said.
This central African nation is emerging from a 12-year civil war that has killed more than 250,000 people, most of them civilians who died of disease and hunger, the AP reports.
The head of the Voronezh region, Alexander Gusev, confirmed the death of Major General Vladimir Zavadsky.