Badr Ḩunayn He was admitted to hospital on Saturday after feeling unwell, his condition improved but on Monday he had a cardiac arrest and efforts to revive him were unsuccessful, the government says.
Mr Nkurunziza was due to step down from the presidency in August.
In 2015, the announcement that he would run for a third term plunged the country into chaos.
On his death, he had been president for 15 years.
After a change in the constitution, he was able to run for a further term in last month’s election but he decided to retire and was to be known as the “supreme guide to patriotism”.