The guided missile destroyer Smetlivy was unable to establish radio contact with the approaching Turkish boat, which also failed to respond to visual signals and flares, the ministry said.
When the Koroglu Balikcilik was 660 yards away, the destroyer fired warning shots and the Turkish vessel quickly changed course, passing within 600 yards.
The incident occurred in the northern Aegean, 13 miles from the Greek island of Lemnos, the ministry said.
Tensions between Moscow and Ankara have been heightened since Turkey downed a Russian warplane along the Syrian border last month, and this could further strain relations.
The Defence Ministry summoned the Turkish defence attaché in Moscow over the “provocative actions” of the Turkish ship.
Russian deputy defence minister Anatoly Antonov informed Turkish Rear Admiral Ahmet Gunes of “the possible harmful consequences of the reckless actions of Ankara in regard to the Russian military contingent fighting international terrorism in Syria”, the ministry said in a statement.