The 64-year-old had held the post since 2006.
“A prominent Russian diplomat has passed away while at work. We’d like to express our sincere condolences to Vitaly Churkin’s family,” the Russian Ministry of Foreign Affairs said in a statement on its official website.
The New York Post reported that Mr Churkin became ill outside the Russian Embassy on East 67th Street at around 9.30am after suffering heart problems.
He was reportedly rushed to New York Presbyterian Hospital, where he later died.
The announcement his death was met with shock when it was delivered during a session at the UN headquarters.
“He was a dear colleague of all os us, a deeply committed diplomat of his country and one of the finest people we have known,” a UN official said.