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.
Nkurunziza died at a 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.
In power since 2005, Nkurunziza was due to be replaced in August by political ally Evariste Ndayishimiye, who was declared earlier this month the winner of a May 20 presidential election.
Nkurunziza's final years in office were racked by turmoil.
His controversial decision to run for a third term in 2015 was condemned by the opposition as unconstitutional and sparked mass unrest. After a failed military coup and a crackdown by security forces, hundreds of thousands of people fled to neighbouring countries to escape the violence.