The Syrian Observatory for Human Rights said the aircraft crashed near the village of Qaminas, southeast of Idlib city, after being hit by a rocket fired by Turkish forces.
Ankara, which supports Syrian armed groups in the rebel enclave in northwestern Syria, acknowledged the attack but did not claim responsibility.
Turkey's defence ministry said it had obtained information that "a helicopter belonging to the regime has crashed" without specifying who was responsible.
At the site of the crash, an AFP correspondent saw the bodies of the two pilots and the mangled remains of the chopper.
President Recep Tayyip Erdogan on Tuesday vowed that Syria would pay a "heavy price" for any attack on Turkish troops, a day after five soldiers were killed in regime shelling.
"The more they attack... our soldiers, they will pay a very, very heavy price," Erdogan told a televised ceremony in Ankara.
He said he would reveal Wednesday the steps to be taken after the flare-up in the Idlib region, the last rebel bastion in Syria.
Ankara said on Monday it had "neutralised" 101 Syria regime forces in response to the deadly artillery attack on its position in Idlib, but that information could not be verified independently.
Neither the UK-based Observatory nor the Syrian government reported any casualties among Syrian troops on Monday.
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