"Two grenades exploded in the city centre... They killed three people and injured several others, probably more than a dozen," said General Godefroid Bizimana.
The bodies of the victims, apparently fruit sellers, were seen lying in pools of blood on the pavement, an AFP journalist said.
The grenade attack is the latest in almost a month of violence in the central African nation, including almost daily street protests in which more than 20 people have died, triggered by President Pierre Nkurunziza's bid for a third term in power.
The crisis, which began in late April after the ruling party nominated Nkurunziza to stand again in the June 26 presidential election, deepened last week when a top general staged a failed coup attempt.
Several grenades have been thrown during street protests, but apparently aimed more to terrorise rather than as in the case of Friday's attack, which was targeted deliberately at a crowd.