The most cancers therapy facility was evacuated after the crash, which occurred close to the famed Tahrir Sq. "We ran to the main entrance of the hospital but it was on fire, so we left through another side door", she said.
The ministry said that the injured were taken to three different hospitals, where they were being treated for wounds and burns.
There was no immediate explanation as to why the crash had caused such a large explosion and officials could not be reached for questions about possible sabotage or whether there had been any explosive materials at the scene.
The health ministry said several people were critically injured in the blast.
"I saw body parts and lots of blood", she said, adding that she believed the fire had burned for an hour.
Egypt's prosecutor general has ordered an investigation to determine the causes of the crash, the AFP news agency reported.
Road accidents are common in Egypt due to high speed and poor road maintenance.
Problems started after the overthrow of Hosni Mubarak, who had been president for almost 30 years. The nation's official statistics company says eight, 000 crashes final 12 months prompted greater than three, 000 deaths and 12,000 accidents.