The bomb exploded on the third floor of the state television and radio building, state TV said. However, while the rebels may have struck a symbolic blow in their 17-month-old uprising against Assad, Information Minister Omran Zoabi said none of the injuries was serious, and the channel continued broadcasting.
Rebels in districts of Aleppo visited by Reuters journalists seemed battered, overwhelmed and running low on ammunition after days of intense shelling of their positions by tanks and heavy machinegun fire from helicopter gunships.
Emboldened by an audacious bomb attack in Damascus that killed four of Assad's top security officials last month, the rebels had tried to overrun the Damascus and Aleppo, the country's commercial hub, near the Turkish border.
But the lightly armed rebels have been outgunned by the Syrian army's superior weaponry. They were largely driven out of Damascus and are struggling to hold on to territorial gains made in Aleppo, a city of 2.5 million.
Damascus has criticized Gulf Arab states and Turkey for calling for the rebels to be armed, and state television has described the rebels as a "Turkish-Gulf militia", saying dead Turkish and Afghan fighters had been found in Aleppo.