The La Fayette stealth frigate, capable of carrying guided missiles, was moving north along the Black Sea west coast, according to the source.
"As of now there is nothing out of the ordinary in her movements. The previous group of NATO ships recently staged exercises in the same region, near the ports of Varna [Bulgaria] and Constanta [Romania]," the source said.
Last week, the NATO Allied Maritime Command said the bloc's ships had completed joint drills with Romanian, Turkish and Bulgarian Navies in the Black Sea.
Moscow has repeatedly criticized NATO for stirring up regional tensions by deploying its military close to Russian borders.