The rival groups clashed, using stones, sticks and knives. Several of the camel and horse riders were dragged from their steeds and beaten.
Pro-government supporters are reported to have pelted their opponents with stones and furniture from the 10th storey of a building overlooking the square.
Elsewhere, a crowd of anti-Mubarak protesters beat at least 10 pro-regime demonstrators with sticks.
They also commandeered five army trucks, pushing them into place to try to form a barricade between themselves and the pro-regime protesters.
The military present on the square refused to take sides, after the army told protesters to go home in the morning.
The confrontations erupted after thousands of Mubarak supporters marched into the square, which has been the focal point of nine days of anti-government protests.
Protesters on both sides began throwing stones at each other, with some of the fiercest clashes breaking out in front of the world famous Egyptian Museum.
Anti-Mubarak protesters accused the leader's National Democratic Party of orchestrating the clashes and showed an AFP reporter four party membership cards they said were taken from demonstrators who began attacking people.
An opposition statement accused plain-clothes police officers and “thugs” had stormed the square.
The clashes came after pro-regime demonstrators staged protests in various parts of Cairo.
In the upmarket Mohandeseen district, an estimated 3,000 people rallied in support of Mubarak, chanting "We don't want you to go," and accusing opposition figure Mohammed ElBaradei of being a traitor.
Earlier Wednesday, a crowd gathered by state TV headquarters, carrying banners reading "Yes to Mubarak, to protect stability," "Yes to the president of peace and stability," and "Those who love Egypt would not drown it."
A witness said organisers were paying people 100 Egyptian pounds (12 euros) to take part in the pro-Mubarak rally, but this could not be confirmed.