Two F-16 warplanes shot down the jet after it failed to heed the warnings within the rules of engagement, state-run Hurriyet Daily News reported.
The jet crashed into tents in Latakia's Yamadi village near the Syrian border where Turkmens are currently staying, according to Turkmen sources. Two pilots were seen landing with the aid of parachutes, the witnesses said.
Video footage showed the plane crashing into mountains in Latakia province.
One of the pilots was killed and the other was captured by Turkmen forces in the region, CNN Turk reported.
Russian helicopters are currently searching the area to reach the pilots as well as the wreckage of the jet, Dogan News Agency reported.
However, the Russian defence ministry said the downed jet, which was at an altitude of 6,000 metres, did not violate Turkish airspace.
The ministry stressed that "throughout its flight, the aircraft remained exclusively above Syrian territory".
Turkey has warned against violations of its airspace by Russian and Syrian aircraft.
Last month, Ankara said Turkish F-16s had intercepted a Russian jet that crossed its border and two Turkish jets had been harassed by an unidentified Mig-29.
The Turkish foreign ministry also summoned the Russian ambassador last week to warn him that there would be "serious consequences" if the Russian air force did not immediately stop bombing "civilian Turkmen villages" in Latakia province.