Syrian state TV announced Hijab's dismissal as government forces appeared to prepare a ground assault to clear battered rebels from Aleppo, the country's biggest city.
President Bashar al-Assad appointed Hijab, a former agriculture minister, as prime minister only in June following a parliamentary election which authorities said was a step towards political reform but which opponents dismissed as a sham.
"Hijab is in Jordan with his family," said the Jordanian official source, who did not want to be further identified.
Syrian TV said Omar Ghalawanji, who was previously a deputy prime minister, had been appointed to lead a temporary caretaker government on Monday.
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, 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 state TV continued broadcasting.
Rebels in districts of Aleppo visited by Reuters journalists seemed battered, overwhelmed and running low on ammunition after days of intense tank shelling and helicopter gunships strafing their positions with heavy machinegun fire.
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.
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 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 U.N. Security Council over how to stop the bloodshed forced peace envoy Kofi Annan to resign last week, his ceasefire plan a distant memory.