Adolphe Nshimirimana was widely seen as the central African nation's de facto internal security chief and even considered the regime's number-two.
Police and witnesses said General Nshimirimana's pick-up was hit by two rockets and sprayed with automatic gunfire in the capital Bujumbura on Sunday morning.
The presidency's communications chief Willy Nyamitwe confirmed that the general, a former army chief of staff and intelligence chief, had been killed.
"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 general's driver was also killed in the attack.
The assassination came just over a week after Nkurunziza was declared the outright winner of a controversial presidential election, 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 people dead in a fierce government crackdown, as well as an attempted coup in mid-May.
Nshimirimana was seen as the mastermind behind the crackdown on the protests as well as a key player in foiling the coup attempt.
African Union Commission chief Nkosazana Dlamini Zuma said in a statement she was "horrified" by the assassination, condemning "this barbaric act that is likely to further destabilise the country".
Soldiers guard a polling station in the Musaga neighborhood of Bujumbura on July 21, 2015 (AFP Photo …
She urged the Burundian government, opposition political parties and civil society "to work very closely together to find a lasting solution to the current crisis".
The European Union's foreign policy chief Federica Mogherini also condemned the attack, warning that it marked "a dangerous escalation of the violence in Burundi".
She urged all parties to return to dialogue to resolve the country's "serious crisis", a spokeswoman said in a statement.
Burundian journalist and AFP correspondent Esdras Ndikumana said he was detained by government security forces at the scene of the murder and badly beaten.
He was then released and hospitalised, with the injuries also including a suspected broken finger.
AFP's global news director Michele Leridon said she was "very shocked" by the attack, adding that the news agency would seek explanations from the Burundian authorities "and an assurance that such an incident will not happen again".
A source in the presidency warned of possible revenge attacks.
"The situation is very serious. The general was somebody who was essential in the system," said the source, who asked not to be named.
Police sources said seven arrests were made, and a source in Burundi's National Intelligence Service, the SNR, said security forces were "nervous".
"You cannot imagine what General Adolphe represented for us," the source said.
"They have declared war and they will see what they get," said another top pro-Nkurunziza general, who asked not to be named.
There was no immediate claim of responsibility for the assassination, although the plotters behind the recent failed coup have since regrouped and have launched a rebellion in the north of the country. They have also been linked to a string of grenade attacks in Bujumbura.
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.