Evgenii Kuznetcov, 54, was thought to be in difficulties about 4pm when other snorkellers noticed him caught in a current and not moving.
He and his wife, Marina, were at Hin Pair, off the mainland in Krabi, a neighboring province to Phuket.
His wife said Mr Kuznetcov suffered from high blood pressure. The cause of his death has yet to be determined.
His body was taken to Phi Phi Hospital.