The local governor, Yucel Yavuz, said an investigation had been launched into the incident - which Pegasus Airlines described in a statement as a "runway excursion".
Images showed the white aircraft left dangling precariously on the cliff face against the backdrop of the crystal clear blue waters of the Black Sea.
According to The Associated Press, no one was hurt in the incident, and everyone on board was evacuated safely.
The Pegasus Airlines had taken off smoothly from the capital Ankara before it landed in Trabzon, reported Reuters.
Plane skids off runway in northern Turkey
Other images from Dogan news agency showed smoke emanating from the trapped plane. "The front of the plane crashed and the back was in the air. There was panic; people shouting, screaming", she said.
The cause of the accident was not yet known and the airport was closed for several hours while authorities investigated.
The airport was temporarily shut before reopening on Sunday morning.