"A number of citizens, including a woman, were killed and others were injured... By terrorist shelling of residential neighbourhoods in Damascus," state television said in a breaking news alert.
It also reported material damage in the heavy rocket fire, but gave no further details on casualties.
The Syrian Observatory for Human Rights, a Britain-based monitoring group, said more than 50 missiles were fired at several central neighbourhoods, killing at least one person.
The group, which relies on a network of sources on the ground, said at least 20 people were injured, with some left in serious condition.
Rights groups have condemned indiscriminate rebel rocket fire into the capital as amounting to war crimes.
The government regularly carries out air strikes against rebel-held areas on the outskirts of Damascus, particularly the Eastern Ghouta region, which is also under regime siege.
