The interior ministry said one car was speeding and collided with the others, causing the explosion late on Sunday, Aljazeera reported.
But why the crash caused such a large explosion was not immediately clear. It also was not clear if the casualties were all from the vehicles.
Videos posted online showed fire tenders trying to control a massive fire that damaged several cars.
The cancer treatment facility was evacuated after the crash, which happened near the famed Tahrir Square.
The health ministry said the injured people were taken to hospitals for treatment.
Egypt's public prosecutor is investigating the cause of the incident, sources told Reuters news agency. There was no official statement indicating that the explosion was an attack.
Sources told Al Jazeera that a team of prosecutors, criminal laboratory and bomb experts have arrived at the scene of the explosion.
Road accidents are common in Egypt. The country's official statistics agency says 8,000 crashes last year caused more than 3,000 deaths and 12,000 injuries.
MNA/PR
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