The gunmen fired at Kararuza's car, killing the Tutsi general and his wife, military officials said Monday.
A bodyguard also died in the attack, while Kararuza's daughter, their driver and another bodyguard were injured, according to a spokesman. The army did not immediately announce details of the attackers.
The general was among few high-ranking Tutsi military officers still close to President Pierre Nkurunziza, an ethnic Hutu with a Tutsi mother.
UN Secretary General Ban Ki-moon condemned the killing, Ban's spokesman Stephane Dujarric said.
"All such acts of violence serve no purpose other than to worsen the already volatile situation in Burundi," Dujarric said. "The secretary general urges that a rigorous and prompt investigation of these events is undertaken."
Fears of war
The general was recently named advisor to Vice President Gaston Sindimwo, also a Tutsi. Previously, the officer served as deputy commander of a peacekeeping force in the Central African Republic.
Kararuza's death follows a year-long spiral of violence and political crisis in Burundi. Last April, Nkurunziza sparked nation-wide turmoil by announcing he would seek a third term as head of state. The instability continues to this day, despite Nkurunziza's disputed victory at the polls.
International observers fear that the conflict might escalate into an ethnic war between Tutsi and Hutu tribes. The latest bloodshed comes as international prosecutors are launching a probe into Burundi's year of violence.
President Nkurunziza condemned Monday's assassination.
In separate attacks on Sunday, a Tutsi police colonel was seriously injured and Human Rights Minister Martin Nivyabandi and his wife managed to avoid a grenade blast while leaving church. A police officer's wife was also killed late on Sunday.
"Those who killed my colleague General Kararuza and [perpetrated] other similar attacks are trying to sow divisions in the army and the police," presidential spokesman Willy Nyamitwe wrote on Twitter.
dj/jlw (AFP, AP, dpa)