They said the vessel’s engine room was damaged in the overnight strike in the Kerch Strait. No-one was hurt.
Ukraine has not publicly commented. But a Ukrainian security service source told the BBC a sea drone had been used.
Saturday’s attack is the second in as many days involving such weapons. Russia, however, has not admitted any damage during Friday’s attack.
Naval drones, or sea drones, are small, unmanned vessels which operate on or below the water’s surface. Research by BBC Verify suggests Ukraine has carried out several attacks with sea drones.