Ukraine's navy said that Russia's border guards rammed one of its tugboats in the Black Sea off Moscow-annexed Crimea on Sunday in "openly aggressive actions."
Russia accused Kiev of illegally entering its waters and deliberately provoking a conflict.
Russia claims the waters off Crimea after annexing the peninsula in 2014.
A Russian border guard ship, the Don, "rammed into our tugboat," the Ukrainian navy said, adding that this caused damage to its engine, outer shell and guardrail.
Russia's ships "carried out openly aggressive actions against Ukrainian naval ships," it said.
It said the ships were continuing on their way "despite Russia's counteraction."
Russia's FSB security service, which oversees the border guard service, said in a statement quoted by Russian news agencies that the Ukrainian ships "illegally entered a temporarily closed area of Russian territorial waters."
It said Ukraine's ships were carrying out "provocative actions" and "their aim is clear: to create a conflict situation in this region."
Ukraine said it gave Russia advance warning of its ships' route, however. Its ships are obliged to take this route to reach the Sea of Azov.
The latest incident comes after the Ukrainian navy in September complained of "acts of provocation" by Russian border guards against its ships taking the same route.
Ukraine has increased the number of navy ships and border guard patrols in the Sea of Azov, which is reached via the Kerch Strait between Crimea and Russia.
Kiev says its naval buildup is due to Russia stepping up controls in the area this year and carrying out lengthy checks on commercial shipping.
Kiev and the West have accused Moscow of deliberately blocking ships from accessing Mariupol, which has vital access to heavy industry in the region.
Mariupol is close to the region of eastern Ukraine controlled by Russian-backed separatists in a conflict that has caused at least 10,000 deaths since 2014.