The Agence France-Presse reported that Shirinsky was found in the swimming pool. The Russian Foreign Ministry has verified the news.
A senior police official in sudan who requested anonymity told AFP that, according to the first elements of the investigation, the track criminal was dismissed.
Embassy staff said he showed signs of a heart attack, and that they called an ambulance but doctors were unable to save him.
"The Russian ambassador died this evening at his Khartoum residence", the Sudanese foreign ministry said in a statement, without giving a cause of death.
His body has been taken to the morgue as local police awaiting instructions from Russian foreign ministry.
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On the first day of the drive, the army said it captured 12 square miles of terrrain and killed 20 Islamic State militants. Last month, Hezbollah concluded a joint counter-terrorism campaign with the Syrian army at Lebanon's highlands of Arsal.
Sudan's foreign ministry expressed its condolences to Russian Federation in a statement, praising Shirinsky's diplomatic efforts.
Born in 1954, Shirinsky has become Russia's ambassador to Sudan since 2013.
Khartoum is the capital of the African country of Sudan.
The Russian ambassador to Turkey, Andrei Karlov, was shot dead by an off-duty Turkish police officer at a photography exhibit in Ankara on December 19, 2016.
He previously served as ambassador to Rwanda, and had diplomatic postings in Egypt, Saudi Arabia and Yemen.
"As soon as we receive detailed information from the Russian embassy staff in Khartoum, we will give information on the circumstances of the death of our colleague", Moscow's foreign ministry reportedly said in a statement.