One crewman suffered non-life-threatening injuries in the incident on Thursday morning, the Turkish coastguard said.
The fire broke out in the engine room of the 600-dwt Turkish-owned Yakamoz-5 (built 1961), which was anchored near Istanbul.
Two lifeboats and two tugs were sent to the scene to begin fighting the fire.
The Saroz Gemicilik tanker had 240 tons of diesel on board, plus 145 tons of other oil.
