"A Syrian plane violated our airspace," Prime Minister Tayyip Erdogan told an election rally of his supporters in northwest Turkey.
"Our F-16s took off and hit this plane. Why? Because if you violate my airspace, our slap after this will be hard," Edrogan.
The rebels have been fighting for control of the Kasab crossing, the border region, since Friday, when they launched an offensive which Syrian authorities say was backed by Turkey's military.
Syria said Turkish air defences shot down the jet while it was attacking rebel forces inside Syrian territory, calling the move a "blatant aggression".
State television quoted a military source as saying the pilot managed to eject from the plane. The Syrian Observatory for Human Rights monitoring group said initial reports from the area said the plane came down on the Syrian side of the border.
Al Manar, the television station of Assad's Lebanese ally Hezbollah, said two rockets had been fired from Turkish territory at the Syrian jet.