Activists say a village school was targeted in rebel-held Idlib.
The UN also warned that the coming winter could be the worst yet in Syria's five-year-long civil war.
Its Syria humanitarian effort head, Jan Egeland, said the brutal conflict had become more ruthless.
He said it was affecting increasing numbers of civilians.
Unicef said that, including the one in Idlib, five Syrian schools had been targeted since 11 October in "simply inhuman" attacks.