The assailants removed barriers blocking traffic and set fire to tents, Ahram Online reported.
Security forces had arrested 53 protesters Wednesday after they entered the square to attempt to remove traffic barriers, MENA reported.
Police said four suspects were arrested in connection with Thursday's attack, al-Masry al-Youm reported. The suspects were armed with a knife and a gun that could fire birdshot.
Two brothers said they were wounded while driving in the square when people with firearms and knives attacked them. One of the men was stabbed in the face, while the other was hit in the upper body by birdshot.
The sit-in protest began Nov. 22 after President Mohamed Morsi issued a decree that critics said put his decisions above judicial review.