The defence ministry confirmed that a search and rescue operation has been launched near the island in the southeast Aegean but did not give other details.
Greek NET television said they collided when the Greek plane rushed to intercept the Turkish jet.
"The two jets collided above Karpathos. We don't know what has happened to the pilots yet," a Greek official told Reuters.
Greek and Turkish fighter planes frequently intercept each other over the Aegean, mostly in areas of disputed airspace.
The two countries, who came close to war as recently as 1996, have considerably improved ties but have not resolved territorial disputes in the Aegean Sea and over the divided island of Cyprus.