The general killed, Adolphe Nshimirimana, was widely seen as the crisis-hit central African nation's de facto internal security chief and even considered the regime's number two.
Police and witnesses said General Nshimirimana's car was hit in an apparent rocket attack in the capital shortly before midday Sunday, and he was later confirmed to have died.
The presidency's communications chief Willy Nyamitwe confirmed the general, a former army chief of staff and intelligence chief, had been killed, as reported by AFP on Sunday.
"I have lost a brother, a companion in the struggle. The sad reality is that General Adolphe Nshimirimana is no longer with this world," he said in a message posted on Twitter.
The assassination comes just over a week after President Nkurunziza was declared the outright winner of controversial elections, securing a third consecutive term despite opposition protests and international condemnation.
Nkurunziza's candidacy was condemned as unconstitutional by the opposition and provoked months of protests that left at least 100 dead, as well as an attempted coup in mid-May.
General Nshimirimana was seen as the mastermind behind the crackdown on the protests as well as a key player in foiling the coup attempt.
There are fears that renewed conflict in the country could reignite ethnic Hutu-Tutsi violence and bring another humanitarian disaster to central Africa's troubled Great Lakes region.
The last civil war in Burundi, which ended in 2006, left at least 300,000 people dead.