The Mirazh, part of the country's Black Sea Fleet, was recently involved in Russia's "peace enforcement" operation which began after Georgia launched an offensive in breakaway South Ossetia on August 8.
Reportedly, it was the Mirazh, which sank a Georgian vessel during an attempted attack on Russian ships near Abkhazia's coast last week.
The vessel was greeted by crowds of people waving Russian flags and fireworks, while a group of students from western Ukraine held banners, which read "Shame" and "Out of here!"
Meanwhile, a high ranking source in the Turkish Naval Forces said that two NATO frigates carrying humanitarian aid for Georgia had entered Black Sea waters.
Ukraine's President Viktor Yushchenko signed a decree last Wednesday requiring prior notification from Russia of all movements by naval vessels and aircraft from the country's Black Sea Fleet base in Ukraine's Crimea.
Ukraine even threatened to refuse Russian vessels entry to the Sevastopol naval base. Russia's Black Sea Fleet uses the Sevastopol base under agreements signed in 1997. Yushchenko announced earlier this year that Ukraine would not extend the lease beyond 2017.