General Prime Niyongabo was heading to his office in the morning when armed men attacked his motorcade.
Burundi's deputy police chief Gen Godefroid Bizimana told the AFP news agency the army chief was unharmed.
Burundi has suffered serious unrest since President Pierre Nkurunziza's decision in April to seek a third term in polls he went on to win in July.
In May he survived a coup attempt.
A senior army general and close aide to the president, Adolphe Nshimirimana, was killed last month in similar circumstances.
Earlier this week the spokesman for a party opposed to President Nkurunziza's third term was shot dead in Bujumbura.
The BBC's Prime Ndikumagenge in Bujumbura says the men who attacked the motorcade on one of the busiest roads in the south of the city were armed with guns and rockets.
Gen Bizimana said that two of the attackers were killed in the clash, a third was arrested and reinforcement had arrived to pursue the others involved, AFP reports
A senior police source, who asked not to be named, told AFP the attackers were wearing military uniforms and travelling in a military vehicle.
"It was sudden and violent. Four bodyguards were killed instantly. He [the army chief] managed to survive only because the driver managed to overtake a bus transporting police officers to work, and the attackers could not keep up," the source said.
At least 100 people have died in protests, mainly in Bujumbura, since Mr Nkurunziza announced his decision seek another term in office.
The government accuses the opposition, which says the third term is illegal, of causing the violence.
The political tensions there have forced tens of thousands people to flee the country this year.