The rockets hit Al-Dabbeet hospital in the Muhafaza district, state news agency SANA said.
Terrorists' rocket fire on other government-held neighborhoods killed another 11 people, it added.
The so-called Syrian Observatory for Human Rights said rebels had fired rockets and shells on government-controlled western districts of the city throughout the day, , AFP reported.
Tuesday's attack comes as diplomatic focus moves to Moscow where the UN envoy for Syria is arriving for talks on restoring a piecemeal cease-fire that would also include Aleppo, Syria's largest city and once commercial center.
The northern metropolis has been hit by a wave of violence that has killed more than 250 civilians since April 22, sparking a diplomatic push by Russia and the United States to end the carnage and restore a teetering truce.