The Syrian military could not immediately be reached for comment.
The Syrian Observatory for Human Rights said the aircraft went down in government territory southwest of Damascus after a missile hit it. Rebels are fighting Syrian government forces in the vicinity.
Two Syrian army officers from the helicopter's crew died, the Britain-based monitor said.
Smoke emanating from the crashed army helicopter. Picture from social media.
Syrian insurgents brought down an army helicopter in southwest Syria on Friday, near the Israel-occupied Golan Heights, a war monitoring group said.