The research ship Liman "sustained a hull breach due to a collision" with the ship Ashot-7, 40 kilometres (25 miles) northwest of the Bosphorus Strait, the ministry said in a statement carried by Russian agencies.
The statement said the crew was not harmed but is "fighting to keep the ship" afloat and that other Russian navy ships and a plane have been dispatched to the scene.
The Russian military said it is trying to identify the owner of the Ashot-7 ship.
In February, military sources told Russian media that it would be observing NATO's Sea Shield exercise in the Black Sea.
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