The investigators said in a report last month that thousands of people had been tortured, suffered sexual abuse or disappeared during political violence.
They also warned of the danger of genocide from the escalating violence.
The decision comes days after Burundi announced plans to withdraw from the International Criminal Court (ICC).
A letter signed by Foreign Affairs Minister Alain Aime Nyamitwe said Pablo de Greiff of Colombia, Christof Heyns of South Africa, and Maya Sahli-Fadel of Algeria were no longer welcome in Burundi.
Their investigation, published in a UN report, had described “abundant evidence of gross human rights violations” possibly amounting to crimes against humanity, by the government of Burundi and people associated with it.
Speaking in New York on Monday, UN spokesman Stephane Dujarric urged Burundi to continue to co-operate with the investigators.
“It’s critical that Burundi and every other country co-operate fully with UN human rights mechanism and that is including working with those representing it,” he said.
Burundi’s announcement to withdraw from the ICC came six months after the Hague-based court said it would investigate ongoing violence in the country.
The African Union (AU) has repeatedly complained that the ICC treats Africans and Africa unfairly.
Burundi descended into political turmoil in April 2015 when President Pierre Nkurunzinza began his bid for a third term.
Since then, more than 500 people have died and at least 270,000 have fled the country.