A car drove at high speed in the wrong direction, crashing into three others outside a cancer hospital in central Cairo, causing an explosion.
Another 47 people were injured, at least three of them critically, a health ministry spokesman added.
President Abdel Fattah al-Sisi sent condolences to families of those killed in the “cowardly terrorist incident”.
“I extend my deepest condolences to the Egyptian people and the families of the martyrs killed in the cowardly terrorist incident in the vicinity of the Kasr al-Aini area yesterday evening,” he wrote in a tribute to the victims on his official social media accounts.
The crash sparked a fire that forced the evacuation of nearby buildings. Images of blazing cars and plumes of smoke have been widely shared on social media.
Khaled Megahed, spokesman for the health ministry, said the wounded were suffering from “several burns of varying degrees”.
Some 78 cancer patients who were being treated inside the hospital have now been transferred to other facilities, he added.
The prosecutor general has ordered an investigation into the causes of the crash, while the police said they suspected it was carried out by Hasm, an armed affiliate of the Muslim Brotherhood.
The explosion caused damage to the structure of the hospital, one witness told Reuters news agency.
Images showed investigators scouring the scene overnight while armed police stood guard.