Footage released by Russia's Southern Transport Prosecutor's Office showed the bow of one tanker completely broken off, with streaks of oil visible in the water.
Both tankers are believed to have drifted before running aground offshore. At least one crew member was reportedly killed, but a rescue operation was able to evacuate the remaining sailors.
The incident took place in the Kerch Strait, which separates Russia from Crimea – the Ukrainian peninsula illegally annexed by Moscow in 2014.