The Eastern Ghouta rebel enclave near Damascus has been bombarded by government forces for the past week.
After the vote in New York, activists said air strikes were continuing.
The vote had been delayed several times since Thursday as members struggled to come to an agreement.
Russia, an ally of Syria's government, wanted changes, while Western diplomats accused Moscow of stalling for time.
Some 500 people are said to have been killed by government forces in the enclave since last Sunday while rebels fire on Damascus has reportedly killed at least 16 civilians.
