The Greek navy said nobody was hurt in the collision late on Monday, the second such incident in a month, which it blamed on "dangerous manoeuvres" by the Turkish boat.
The Greek boat, which was financed with European funds "to monitor Greek seas and European borders", suffered damage, the navy said.
The incident occurred near the uninhabited Imia islets, just off the Turkish coast and a historic flashpoint in a long-running demarcation dispute.
Greek Prime Minister Alexis Tsipras complained about the latest incident to his Turkish counterpart Binali Yildirim, who initiated a phone call between the two on Tuesday.
Tsipras told Yildirim that such collisions undermine relations between the two countries as well as between Turkey and the EU, and violate international law, the Greek prime minister's office said in a statement.
Tsipras stressed "the need to immediately stop Turkish violations" of Greek territory in the Aegean and "de-escalate tensions", the statement said.