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. Greek media said Mr Malanin had failed to report for work on Monday and did not answer his phone. He lived alone on a heavily guarded street.
Police told the Associated Press that there were no signs of harm on Mr Malanin's body, but an investigation had been launched, 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 last month.