The attacks come amid a spike in violence in Syria and a particularly bloody week nearly two years after an uprising against Assad's regime started.
Video broadcast on Syrian state TV showed several floors of the targeted building collapsed in a government-controlled area of the city, Syria's largest urban center and main commercial hub. A man was seen carrying a baby out the damaged building and another man was seen clutching his head as blood ran down his forehead.
The number of dead and wounded was not immediately clear.
It was the second time in a week that the government accused rebels of firing rockets.
On Tuesday, 87 people were killed in twin blasts at Aleppo University. Each side blamed the other for that attack. The regime said rebels hit the university with rockets. Rebels said the deaths resulted from regime airstrikes.
The state-run SANA news agency blamed the morning attack on terrorists, a term the regime uses for rebels. But the Local Coordination Committees of Syria, an activist group, and the Aleppo Media Center, a network of anti-regime activists, accused the government of launching an airstrike.
State TV showed residents looking for people buried in the rubble. At least one injured person on a stretcher was seen being carried away in a Red Crescent ambulance.
On Thursday, opposition activists said pro-government militia swept through a town in central Syria, torching houses and killing more than 100 people.
Also on Friday, fighting between Syrian rebels and Assad's loyalists flared in a Palestinian refugee camp in Damascus, killing 12 people and wounding at least 20 others, a U.N. refugee agency said. Children were among the casualties, according to a statement issued by the U.N. Relief and Works Agency. The agency called on both sides to "pull back from civilian areas, including refugee camps."
The Palestinian camp called Yarmouk has been the scene of heavy clashes between rebels and regime loyalists since mid-December, when opposition fighters moved into the camp during an attempt to storm the capital.
About half of Yarmouk's 150,000 residents have fled since fighting erupted in mid-December, according to UNRWA, which administers Palestinian camps in the Middle East. Some sought refuge in neighboring Lebanon, and others found shelter in UNRWA schools in Damascus and other Syrian cities.
Dozens have been killed in the fighting, although the United Nations did not provide an exact figure of casualties in Yarmouk violence, which has included airstrikes and artillery shelling from the Syrian military.
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