Turkish jets, after taking off from the south of the country, shot down the Syrian craft that had crossed the border into the Hatay region, a Turkish general staff source told the DHA news agency.
"The craft was struck twice but there is no clarity over what it was. Once the identity of the craft has been made clear, the public will be informed," the source was quoted as saying.
Other sources quoted by Turkish media said it could have been a plane, helicopter or unmanned drone that had been shot down by the Turkish F-16s.
Syria meanwhile vehemently denied it could have been a manned aircraft.
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"It is not true that Turkish fighter jets shot down a Syrian plane. What was shot down was a small drone flying nearby," Syrian state TV said, citing a military source.
Turkish President Recep Tayyip Erdogan has emerged as one of the main opponents of Syrian President Bashar al-Assad, saying his exit is key to solving the conflict.