The head of the Britain-based Syrian Observatory for Human Rights said it was not immediately clear if the strike was carried out by a Syrian or Russian aircraft.
Rami Abdel Rahman said the attack hit "a hospital located in a cave in the Abdeen region in southern Idlib province, causing huge damage and knocking it out of action".
"Five staff members were wounded and were pulled from the rubble, but four more are still trapped beneath it," Abdel Rahman said.
Idlib is controlled by a rebel alliance that includes a former Al-Qaeda affiliate, and is regularly targeted by both the Syrian government and its Russian ally.
Earlier this month, a suspected chemical attack hit the town of Khan Sheikhun in Idlib, killing dozens of civilians including children.
Much of the international community blamed the Syrian regime for that attack, and three days later 59 cruise missiles fired from US warships targeted the airbase from where the attack was launched.
Abdeen, where the hospital was hit on Saturday, is eight kilometres (five miles) from Khan Sheikhun.
The Observatory said regime forces fired a rocket at the Abdeen region after the air strike, killing a young man working in a field.
More than 320,000 people have been killed in Syria since the conflict began in March 2011 with anti-government demonstrations.