The Turkish military says it warned a Syrian warplane four times that it was approaching Turkey's airspace before shooting it down.
The military said in a statement that a second Syrian plane heeded the warnings and turned back.
Turkey's Prime Minister Recep Tayyip Erdogan warned such action by Syria merited a "heavy response". But Syria accused Turkey of "blatant aggression", saying the plane had been over Syrian territory at the time.
The incident reportedly occurred in an area where Syrian rebels and government forces have been fighting for control of a border crossing. Turkey and Syria - once allies - share more than 800km of border, the BBC reports.
Turkey has broadly sided with the rebels in Syria's war since October 2011. However, Turkish forces launched artillery strikes on Syrian targets in late 2012 after the Syrians shot down a Turkish jet.
Speaking at a rally of supporters, Mr Erdogan congratulated the air force on its actions on Sunday.
"A Syrian plane violated our airspace. Our F-16s took off and hit this plane. Why? because if you violate my airspace, our slap after this will be hard."
A Syrian military source, quoted by state television, said Turkish air defences had shot down a Syrian jet as it attacked rebels on Syrian territory - an act of "blatant aggression".
The Syrian Observatory for Human Rights - a British-based activist group - said initial reports from the area suggested the plane came down on the Syrian side of the border.
"Turkish air defences targeted a Syrian fighter-bomber as it struck areas of the northern province of Latakia. The plane caught fire and crashed in Syrian territory," the Observatory said.
According to one report, the plane's pilot was able to eject.
In a media statement on the incident, the Turkish General Staff said two Syrian military jets were involved, and that they had been "warned four times that they were approaching Turkish airspace".
The Turkish general staff said one of its control centres detected two Syrian MIG-23s around 1pm on Sunday and warned them four times after they came close to the Turkish border.
One plane entered Turkish airspace at Yayladagi, east of the Kasab border crossing, it said. A Turkish F-16 fired a rocket at the Syrian jet and it crashed around 1200 metres inside Syrian territory.
In September last year, Turkey said it had shot down a Syrian helicopter close to its border. Deputy Prime Minister Bulent Arinc said the aircraft was engaged by fighter jets after violating Turkish air space.
A Turkish fighter jet was shot down by Syria over the Mediterranean in June 2012 after Syrian forces said it had entered the country's airspace.
After this incident, the Turkish government announced that it had revised its military rules of engagement towards Syria and would consider every military element approaching its border from Syria as a threat.