They said the four gunmen also vandalised vehicles in the area, including those of the US Embassy, early on Monday. The officials spoke on condition of anonymity because they were not authorised to talk to the media.
The US Embassy, which is off Tahrir Square, said vandals attacked an Embassy van, slashing its tires and breaking a window.
It warned US citizens in a warden message against going to the square in downtown Cairo, where New Year's celebrations are planned later. The square was the centre of Egypt's uprising two years ago.
The sit-in was to protest against Islamist President Mohammed Morsi's moves to pass a disputed constitution.