The Turkish army said the plane was shot down by two Turkish F-16s after violating Turkish airspace 10 times within a five-minute period.
With a major diplomatic crisis looming between two states on opposing sides in the Syria conflict, Russia insisted the jet was all the time inside Syrian airspace and condemned the downing as "a very serious incident".
Turkish media said one pilot had been captured by rebel forces in Syria after both ejected by parachute while Syrian opposition sources said one was dead and another missing.
The presence of aircraft from Russia, the United States, France, Turkey and a clutch of Gulf states in Syrian skies had long raised fears of an incident that could quickly escalate into a major diplomatic and military crisis.
"A Russian Su-24 plane was downed under the rules of engagement because it violated Turkish airspace despite the warnings," the Turkish presidency said.
Turkey has summoned the Russian envoy to Ankara over the incident, which comes on the eve of a visit by Russian Foreign Minister Sergei Lavrov to the country.
"Presumably as a result of firing from the ground, an Su-24 plane of the Russian forces crashed in the Syrian Arab Republic," Russian news agencies quoted the defence ministry as saying.
"It is a very serious incident," Kremlin spokesman Dmitry Peskov told reporters.
The Turkish army said that the downing took place over the Yayladagi district of Turkey's Hatay province on the border with Syria.
"The plane violated Turkish air space five times in 10 minutes despite warnings," the army said in a statement, adding it was shot down by at 0724 GMT "according to the rules of engagement".
"NATO is monitoring the situation closely. We are in contact with Turkish authorities.
