Reports say they were protesting against a US-made film that is allegedly insulting to the Prophet Muhammad, and set fire to the building.
The building is said to have burnt down. It is thought nobody was in the consulate at the time.
Earlier, protesters in Egypt breached the wall at the US embassy in Cairo and tore down a flag over the film.
The film that sparked the protest is said to have been produced by US pastor Terry Jones and co-produced by some Egyptian Copt expatriates.
In the Cairo incident, the American flag, which was flying at half mast to mark the 9/11 attacks, was replaced by an Islamist banner.
Thousands of protesters had gathered outside the US embassy in the Egyptian capital.
Egyptian protesters condemned what they said was the humiliation of the Prophet of Islam under the pretext of freedom of speech.