There are conflicting reports on the casualty toll from the incident off the Ukrainian city of Sevastopol, but officials in Ukraine said one crewman was injured.
The Russian navy command said the incident was under investigation but, according to preliminary reports, the passenger vessel had strayed into a restricted test area.
The incident is the third involving former Soviet military hardware in the past five days.
On Thursday, a ground-to-ground missile fired by Ukrainian troops in a training exercise hit a block of flats in the central town of Brovary, killing three people, wounding five and leaving nearly 100 homeless.
In another incident on Friday, a stray Russian missile exploded near a village in Kazakhstan.
Port lease
Ukrainian Defence Minister Oleksandr Kuzmuk said one person was injured aboard the Vereshchahyn, which was en route from Istanbul to the Ukrainian port of Skadovsk, when it was hit above the waterline.
"The ship was in the area closed for navigation and dangerous for traffic when a rocket-firing exercise was taking place," Russian navy spokesman Igor Dygalo said.
Ukraine leases about 80 per cent of the Sevastopol naval base to Russia under an agreement to share out resources of the former Soviet navy.
Admission
Mr Kuzmuk has now acknowledged that an off-course tactical missile caused Friday's blast in Brovary, near the Ukrainian capital Kiev.
The Soviet-made Tochka-U surface-to-surface missile was fired during military training 130km (80 miles) away, and missed its target before hitting the block of flats.
"I would like to express my condolences to the relatives and present my apologies to all the injured and to those who suffered emotional trauma and material losses from this tragedy," Mr Kuzmuk said.
Initially, the Defence Ministry denied the missile hit the block, saying a crater found near the rocket's intended target proved it stayed on course.
Before reports came in of an explosion in Brovary, television channels showed pictures of the missile roaring off a launch truck and a general passing out gifts to soldiers to reward their "success" in the annual test.
"I personally did not believe that it was caused by a practice shot from the range - we had such a strong belief in this type of missile," said Mr Kuzmuk.
Safety concerns
All military exercises with missile launches have been halted pending checks by safety officials. Computer error and rudder malfunction are being mooted as possible causes of the poor targeting.
Kazakhstan has said it will ask Russia to suspend missile tests at its military site near the Caspian Sea after a Russian Strizh-3 missile flew off course last Friday to crash near a village.
No casualties were reported.
The BBC Moscow correspondent says that these incidents are bound to raise to concerns about the safety standards, levels of maintenance and training of Russian and Ukrainian missile forces.
Mr Kuzmuk said Ukraine owns more than 500 Tochka-U missiles but the service-life of most have expired.
He added that Ukraine's armed forces would continue to operate the missiles.