His wife Denise was airlifted for coronavirus treatment in Kenya on May 30, prompting some suspicion about the President’s true cause of death.
Nkurunziza was due to leave office in August after a controversial 15-year term marked by claims of repression and human rights abuses.
“Burundi has lost a worthy son of the country, a president of the republic, a supreme guide of national patriotism,” government spokesperson Prosper Ntahorwamiye said in a statement.
Nkurunziza, who ruled the tiny East African nation for three terms, was due to leave politics after elections in May.
According to the statement, Nkurunziza had attended a volleyball match on Saturday afternoon and was taken to hospital that evening after falling ill.
Although he appeared to recover on Sunday and spoke to those around him, he suddenly deteriorated on Monday morning.
He then suffered a heart attack and despite an immediate resuscitation attempt, doctors were unable to revive him.
He died in the Natwe Turashoboye hospital in Karuzi, eastern Burundi.
The government said there would be a period of national mourning for seven days from Tuesday and that flags would be flown at half-mast.
Books of condolences also would be made available.
Nkurunziza came to power in 2005 soon after a civil war that resulted in the death of approximately 300,000 people.
The war had pitted the majority Hutu ethnic group against the minority Tutsi. The Arusha peace accords introduced power-sharing quotas, with the aim of protecting the Tutsis.
Over the years, however, the ruling party – the National Council for the Defence of Democracy-Force for the Defence of Democracy (CNDD-FDD) – had chipped away at the conditions of the agreements.
When Nkurunziza, a Hutu, announced in 2015 his decision to seek a third term in office, despite a two-term limit set by the accords, civil unrest broke out.
His subsequent election victory unleashed a crisis that led to hundreds of people being killed and hundreds of thousands fleeing.
His rule came to be characterised as repressive, with the UN warning in 2019 that people in Burundi were living under a reign of terror, especially in the run-up to the 2020 elections.
In 2019 changes to the constitution were approved that would have allowed him to potentially remain in power until 2034; but he surprised many by deciding not to run for re-election.
However, in the run-up to elections in May, numerous organisations documented human rights abuses by his government including abductions, torture, killings and harassment of the opposition and the media.
Just before the elections Nkurunziza refused independent observers and expelled World Health Organization (WHO) officials who were assisting with the COVID-19 pandemic.
When he relented and allowed observers, he demanded they remain in quarantine, rendering them unable to perform their duties on voting day.
Nkurunziza often made claims that God would save Burundians from the disease and allowed religious, sports and cultural events to continue regardless.
Details of his funeral would be announced in due course, the government said.