Andrey Malanin, 54, was found dead on his bathroom floor by another member of embassy staff, a police official said.
According to the embassy`s website, Mr Malanin was the head of the consular section.
Police have launched an investigation and the authorities were awaiting a report from the coroner, but there was apparently no evidence of a break in.
"At first sight, we are talking about natural causes," the police official said.
Police told the Associated Press that there were no signs of harm on Mr Malanin`s body, but that a murder investigations unit had been called in because of his diplomatic status.
The death comes three weeks after Russia`s ambassador to Turkey, Andrei Karlov, was assassinated by a riot police officer while speaking at a photo exhibit in Ankara.
/The Independent/
Senior Russian diplomat found dead in Athens apartment, say Greek police
10 January 2017
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A senior diplomat at Russia`s embassy in Athens has been found dead in his apartment, Greek police say, adding that at "first sight" he appears to have died from natural causes.
