The television said a "suicide bomber in a car packed with explosives" carried out one of the attacks on a police station, flattening a nearby food distribution centre. The second bombing targeted an intelligence base.
The report showed mangled bodies in pools of blood in the street outside rows of shattered buildings. Emergency workers held up body parts, including hands, feet and a torso. State television, which said soldiers were among the casualties, blamed the attacks on "armed terrorist gangs".
The channel aired the footage live from the site of the blasts, with bulldozers quickly deployed to clear away shattered concrete strewn across a broad avenue.
Several people who were interviewed denounced Turkey and Qatar for not standing by the regime in Syria as it seeks to put down a revolt that broke out last March. Rami Abdel Rahman, head of the Britain-based Syrian Observatory for Human Rights, told AFP there were two blasts in the northern city, after earlier reporting a total of three.
Aleppo has been largely spared the unrest that has rocked Syria for nearly a year, leaving more than 6,000 people dead according to rights groups. Today's blasts were the biggest since two suicide bombings in Damascus, one of which killed 44 people in December and the second 26 people in January.