The ship, identified as the 'Liman', collided with the Togo-flagged 'Youzarsif H', the coastal safety authority said on its website.
Turkish authorities dispatched a tugboat and three fast rescue vessels, it said. Turkish shipping agency GAC said separately that the collision was caused due to fog and low visibility.
Broadcaster NTV said the collision occurred 18 miles (29 km) from Kilyos village, on the Black Sea coast just north of Istanbul.
Turkey's Bosphorus Strait, which cuts through Istanbul, is one of the world's most important waterways for transit of oil and grains. The 17-mile waterway connects the Black Sea to the Mediterranean.
(Reporting by Tuvan Gumrukcu and Can Sezer, Editing by Dominic Evans and David Dolan)