"The Russian ambassador died this evening at his Khartoum residence," the Sudanese foreign ministry said in a statement, without giving a cause of death.
"He was found dead in the swimming pool of his residence at 7:05 pm (local time)," police spokesman Omar al-Mokhtar told AFP.
"Preliminary investigation shows that his death was natural," he said, as an embassy spokesman said it was apparently was caused by a heart attack.
A diplomatic source also said that the Russian envoy, who was born in 1954 and served for 40 years in the diplomatic service, was found dead in the swimming pool of his residence in north Khartoum.
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The press secretary at Russia's embassy, Sergei Konyashin, said there were signs that the ambassador had suffered an heart attack.
"Mirgayas Shirinsky was found in his residency in a suburb of Khartoum with signs of an acute heart attack," Konyashin told Rossiya-24 TV.
"Doctors were called but they didn't manage to save him."
Mokhtar said Sudanese officials had taken Shirinsky's body to a morgue in the capital and were awaiting instructions from the Russian foreign ministry.
He studied at Moscow Institute of International Relations and had been appointed as ambassador to Khartoum in 2013, having previously served as ambassador to Rwanda.
Shirinsky's long diplomatic career also included postings in Egypt, Saudi Arabia and Yemen.