The decree, shared online Sunday by Burundi's UN ambassador and other officials, could lead to more unrest in the East African country that saw deadly political violence after the president's disputed decision in 2015 to seek a third term.
Opposition and human rights groups have called the referendum a plot by Nkurunziza to stay in power for life.
The proposed changes to the constitution include extending a presidential term from five years to seven. Nkurunziza's current term expires in 2020.
At least 1,200 people were killed and more than 400,000 fled the country in the chaos after Nkurunziza's decision in 2015 to run for a third term. In November, International Criminal Court judges authorized an investigation into allegations of state-sponsored crimes including murder, rape and torture, announcing the decision shortly after Burundi became the first country to formally quit the court.
The referendum in May will leave Burundians more divided, said Hussein Radjabu, a former secretary-general of the ruling party.
"The ruling party is also divided on the matter, so we are likely to see more bloodshed in Burundi as people opposed to lifting term limits will be killed," Radjabu told The Associated Press.
Human rights activists say some opposing the referendum already have been arrested. Others have fled into exile, said local activist Vital Nshimirimana.
Nkurunziza rose to power in 2005 following the signing of the Arusha accords to end Burundi's 13-year civil war that killed about 300,000 people. He was re-elected unopposed in 2010 after the opposition boycotted the vote. Nkurunziza said he was eligible for a third term because lawmakers, not the people, had chosen him for his first term, but critics called the move unconstitutional.