President Vladimir Putin is said to be “deeply upset” by the death, and paid tribute to Mr Churkin’s “professionalism and diplomatic talent”.
The Russian foreign ministry gave no details of the circumstances of the death of the 64-year-old, but one report said he had fallen ill with a heart condition.
“The outstanding Russian diplomat passed away at his work post,” said a statement from the foreign ministry.
“We express our deep condolences to the relatives and close family,”
Farhan Haq, deputy spokesman for the UN secretary-general’s office, said: “He has been such a regular presence here that I am actually quite stunned.
“Our thoughts go to his family, to his friends and to his government.”
Mr Churkin, who would have celebrated his 65th birthday on Tuesday, has been Russia’s permanent representative to the UN since 2006.
— MFA Russia 🇷🇺 (@mfa_russia) February 20, 2017
Russia’s deputy UN ambassador Vladimir Safronkov said Mr Churkin had become ill in his office at Russia’s UN mission and was taken to Columbia Presbyterian Hospital where he died.
Mr Churkin, who spoke Russian, Mongolian, English and French, was considered Moscow’s great champion at the UN.
He had a reputation for a sharp wit and quick repartee, especially with his American and Western counterparts.
He was previously ambassador at large and had earlier served as the foreign ministry spokesman.
In October, Mr Churkin defended Russia against accusations it was bombing civilian targets during the offensive in the Syrian city of Aleppo.
He said Russia regretted civilian casualties and was “careful about selecting targets”.
When the US envoy at the time, Samantha Power, accused Russia of atrocities in Syria, Mr Churkin said she was acting like Mother Teresa and had forgotten her own country’s track record in the Middle East.