UN report detailed widespread and systematic abuses including extrajudicial executions, forced disappearances, torture and sexual violence.
Last year, Burundi formally announced it was withdrawing from the court, with the move set to take effect on October 27.
In its report Monday, the commission put blame for the likely crimes against humanity in Burundi at "the highest level of the state".
The UN investigators said they were drafting a confidential list of suspected perpetrators of crimes against humanity, along with detailed information about the acts they are accused of committing or ordering.
UN investigators on Monday accused Burundi's government of crimes against humanity, including executions and torture, and urged the International Criminal Court to open a case "as soon as possible".
The United Nations Commission of Inquiry on Burundi said it had "reasonable grounds to believe that crimes against humanity have been committed and continue to be committed in Burundi," pointing a finger at "the highest level of the state".
The three investigators, appointed by the Human Rights Council last September, described a "climate of fear" in the crisis-hit the country.
The report detailed widespread and systematic abuses including extrajudicial executions, forced disappearances, torture and sexual violence.
"We are struck by the scale and the brutality of the violations," commission president Fatsah Ouguergouz said in a statement.
Decrying impunity in Burundi and the "strong likelihood that the perpetrators of these crimes will remain unpunished," the investigators asked "the International Criminal Court to open an investigation ... as soon as possible".
If it wants to follow that advice, the ICC will indeed need to move quickly: last year, Burundi formally announced it was withdrawing from the court, with the move set to take effect on October 27.
After that date, the ICC can only open a case if asked to do by the Security Council.
President responsible?
Burundi was thrown into a political crisis in April 2015 when President Pierre Nkurunziza decided to run for a third term that his opponents said was unconstitutional. He won elections in July that year which were boycotted by the opposition.
Between 500 and 2,000 people have been killed in clashes in the country, according to UN and NGO sources. More than 400,000 people have fled and dozens of opposition activists have been forced into exile.
In its report Monday, the commission put blame for the likely crimes against humanity in Burundi at "the highest level of the state".
The perpetrators included members of Burundi's National Intelligence Service, including high-ranking officers, the national police, military officials and members of the ruling party's youth league, the Imbonerakure, investigators said.
Nkurunziza himself, surrounded by a close-knit circle of "generals", was behind "big decisions, including ones that led to serious human rights violations," it said.
Armed opposition groups were also responsible for rights violations in Burundi, the report said, noting that these abuses had been more difficult to document.
List of perpetrators
The UN investigators were never permitted to enter Burundi, forcing them to conduct their probe from neighbouring countries, where they interviewed more than 500 victims and witnesses.
They said they were drafting a confidential list of suspected perpetrators of crimes against humanity, along with detailed information about the acts they are accused of committing or ordering.
The UN is prepared to share the list with any credible judicial body, the report said.
Monday's report meanwhile said that despite a range of abuses against the Tutsi minority, there was currently no evidence of genocide in Burundi, as widely feared.
But the commission said it remained deeply concerned by ethnically-loaded comments made by state and ruling party officials.
"While this discourse does not constitute direct incitement to commit genocide, it nonetheless contributes to create a climate of dangerous hatred and to terrorise the population, and could revive ethnic tensions," it warned.
Burundi suffered a civil war from 1993 until 2006 between majority Hutus and minority Tutsis, which claimed an estimated 300,000 lives.
The current unrest has also sparked fear of a wider crisis in Africa's volatile Great Lakes region, with the 1994 genocide in neighbouring Rwanda having been fuelled by similar ethnic tensions.
