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Social media users posted footage of cars ablaze at the scene and of patients being evacuated from the Cancer Institute, after the pile-up.
The blast caused a fire in the hospital, where at least 54 patients were evacuated to other hospitals. The fire was later brought under control, with television footage Monday morning showing shattered windows and doors.
The incident was reported to be the result of a pile-up but the cause of the large explosion that followed the crash wasn't explained.
Egypt's interior ministry later claimed that one of the vehicles was filled with explosives - believed to have been stolen from Monufia Governorate several months earlier.
The health ministry did not say if hospital patients or staff were among the casualties.
Egypt's prosecutor general has ordered an investigation to determine the causes of the crash.
Although a political motive was not immediately named, Cairo described it as an "act of terrorism" and pointed to the shadowy Hasm organisation as being behind the alleged attack.
Hasm has previously claimed responsibility for attacks on security forces and officials, including an attempted assassination of former Egyptian Grand Mufti Ali Gomaa.
Egyptian authorites rounded up members of Hasm after a bomb blast injured 17 people near the Giza pyramids in May.
The Egyptian government says Hasm is the militant wing of the Muslim Brotherhood but the group has distanced itself from the armed movement.
A seperate insurgency is raging in the northern Sinai by militants alligned to the Islamic State group.
Agencies contributed to this report.
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