Turkish F16s warned the jet over the airspace violations before shooting it down, the military official told Reuters.
Footage from private broadcaster Haberturk TV showed a warplane going down in flames in a woodland area, a long plume of smoke trailing behind it. The plane went down in area known by Turks as "Turkmen Mountain" in northern Syria near the Turkish border, Haberturk said.
Separate footage from Turkey's Anadolu Agency showed two pilots parachuting out of the jet before it crashed.
Russia has repeatedly carried out air strikes in Syria in defence of President Bashar al-Assad. Russia’s defence ministry was not immediately available for comment.
Turkey called this week for a U.N. Security Council meeting to discuss attacks on Turkmens in neighbouring Syria, and last week Ankara summoned the Russian ambassador to protest the bombing of their villages.
Ankara has traditionally expressed solidarity with Syrian Turkmens, who are Syrians of Turkish descent.
Turkish Prime Minister Ahmet Davutoglu has spoken with the chief of military staff and the foreign minister about the developments on the Syrian border, the prime minister's office said in a statement, without mentioning the downed jet.
He has ordered the foreign ministry to consult with NATO, the United Nations and related countries on the latest developments, his office said.