The official says an assailant attacked the American with a knife as he was standing in front of the embassy building in the Cairo suburb of Garden City today.
The official says the American was rushed to a nearby hospital. He says police arrested the attacker who is now being interrogated. The official spoke on condition of anonymity as he was not authorised to talk to the media.
Motives for the attack remained unclear.
Crime has surged in Egypt, including armed robberies, rape and assaults, over the past two years since the 2011 uprising that toppled Hosni Mubarak.