President Bashar al-Assad had appointed the former agriculture minister as prime minister in June, following elections in May, Sky News reported.
Conflicting reports from Syrian state TV claimed Hijab was "dismissed" as he was about to announce his support for the opposition.
In a statement read out on Al Jazeera TV, a spokesperson for Hijab said: "I announce today 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."
Hijab was a leading Sunni Muslim in Assad's government. His home province of Deir Ezzor has been one of the key battlegrounds of the conflict, Sky News said.
Omar Ghalawanji, the deputy prime minister, has been named as a temporary replacement.
According to the telegraph, Hijab joined the rebels in protest against the "genocide" Assad was carrying out against his own people.
He said his defection comes at a time "when Syria is passing through the most difficult war crimes, genocide, and barbaric killings and massacres against unarmed citizens".
A government source in Jordan told the British daily: "Hijab is in Jordan with his family."
Turkish state news agency Anatolia also reported that a Syrian brigadier general and five high-ranking officers have also fled to Turkey to support the rebels.
Meanwhile, five people were wounded in a bomb blast at one of Syria's state television and radio buildings in Damascus.
Information Minister Omran al-Zoabi said there were no deaths in the bombing of the state TV buildings in the heavily protected Omayyad district of Damascus.
"It is clear that the blast was caused by an explosive device. Several of our colleagues were injured, but there were no serious injuries, and no dead," the minister said.
The blast hit the third floor of the building, but the TV network remained on the air despite the bombing.