Syrian state television said Mr Hijab had been fired, but an official source in Amman said the dismissal followed his defection to neighbouring Jordan with his family.
A statement released by Mr Hijab said: "I announce my defection from the killing and terrorist regime and I announce that I have joined the ranks of the freedom and dignity revolution. I announce that I am from today a soldier in this blessed revolution."
Syrian state TV announced Mr Hijab's dismissal as Government forces appeared to prepare a ground assault to clear battered rebels from the city of Aleppo.
Mr Assad appointed Mr Hijab, a former agriculture minister, as prime minister in June after a parliamentary election which authorities said was a step towards political reform but opponents dismissed as a sham.
A Jordanian official confirmed Mr Hijab was in the country and had defected before the announcement of his sacking.
Syrian TV said Omar Ghalawanji, who was previously a deputy prime minister, had been appointed to lead a caretaker government yesterday.
Earlier in the day, a bomb blast hit the Damascus headquarters of Syria's state broadcaster as troops backed by fighter jets kept up an offensive against the last rebel bastion in the capital.
The bomb exploded on the third floor of the state television and radio building. However, while the rebels may have struck a symbolic blow in their 17-month-old uprising against Mr Assad, Information Minister Omran Zoabi said none of the injuries was serious, and state TV continued broadcasting.
In Aleppo, rebels seemed overwhelmed and running low on ammunition after days of intense tank shelling and helicopter gunships strafing their positions with heavy machinegun fire. They were largely driven out of Damascus and are struggling to hold on to territorial gains made in Aleppo, a commercial hub with a population of 2.5 million.
Damascus has criticised Gulf Arab states and Turkey for calling for the rebels to be armed, and state TV has described the rebels as a "Turkish-Gulf militia", saying dead Turkish and Afghan fighters had been found in Aleppo.
Paralysis in the UN Security Council over how to stop the bloodshed forced peace envoy Kofi Annan to resign last week, his ceasefire plan in disarray.
The violence has already shown elements of a proxy war between Sunni and Shi'ite Islam which could spill beyond Syria's border. The rebels claimed responsibility for capturing 48 Iranians in Syria, forcing Tehran to call on Turkey and Qatar – major supporters of the rebels – to help secure their release.
Yesterday, Syrian army tanks shelled alleyways in Aleppo where rebels sought cover as a helicopter gunship fired heavy machinegun fire.
Snipers ran on rooftops targeting rebels, and one of them shot at a rebel car filled with bombs, setting the vehicle on fire. Women and children fled the city, some crammed in the back of pick-up trucks, while others walked, heading to relatively safer rural areas.
Rebel commanders say they anticipate a major Syrian army offensive in Aleppo and one fighter said they had already had to pull back from some streets.
State TV said Mr Assad's forces were "cleansing the terrorist filth" from the country. Around 18,000 people have so far been killed in the conflict.