A gangster killed Burundi';s minister of environment and water, Emmanuel Niyonkuru, earlier on Sunday.
Police affirmed such as the first senior government figure to be ambushed in nearly two years of political violence.
The police spokesman, Pierre Nkurikiye said in a tweet that Niyonkuru was attacked as he travelled home in the capital Bujumbura.
Violent protests occurred early in 2015 after President Pierre Nkurunziza said he would seek a third term; a move opponents said violated the constitution and a tranquil deal that ended an ethnically charged civil war.
At least 450 people have died in conflict between protesters and security forces, revengeful killings and a failed coup, stoking fears of wider unrest in a region still haunted by the 1994 genocide in neighbouring Rwanda.
"The minister of water and environment was shot ... as he was getting home," Nkurikiye said.
Four people had been apprehended for interrogation, including the owner of a bar that Niyonkuru visited regularly alongside his residence’s two security officers, together with a woman who was with the minister when he was murdered.
President Nkurunziza offered condolences to the family and all Burundians after stating on Twitter that the minister had been ambuscaded.
Nkurunziza won re-election in July 2015 in a poll largely boycotted by the opposition.
Elsewhere in Burundi, police said seven people were injured when a strange attacker threw a grenade in a church where people were praying.
That attack erupted on Saturday night in Rugazi district, 40 km (25 miles) north of Bujumbura.
The police spokesperson told Reuters that “the church where the attack took place was not registered with the government and had been erected illegally”.
“Its leader had been detained for investigation,” he added.