Some of the wounded had blood streaming down their faces and many had to be carried out of the square by fellow protesters to waiting ambulances.
Human rights activists accused police of using excessive force.
One prominent activist, Malek Mostafa, lost his right eye from a rubber bullet, said Ghada Shahbender, a member of the Egyptian Organization for Human Rights.
At least four protesters were injured in the eyes as a result of what Shahbender said were orders to target protesters’ heads.
“It is a crime,” she said. “They were shooting rubber bullets directly at the heads. … I heard an officer ordering his soldiers to aim for the head.”
A videojournalist for the Egyptian newspaper Al-Masry al-Youm, Ahmed Abdel-Fatah, was also hit in the eye by a rubber bullet and was undergoing surgery.
Police arrested 18 people, state TV reported, describing the protesters as rioters.
Protests were also held Saturday in the Red Sea port city of Suez, where a crowd of thousands attacked a police station, with some hurling firebombs at the building, said protester Ahmed Khafagi.
In Alexandria, hundreds of people threw stones at the main security headquarters, said protester Ahmed Abdel-Qader. He said it felt like the revolution was starting all over again.
“We only managed to bring down the head of the regime. The rest of the tree is still standing,” he said.
A day earlier, tens of thousands of Islamists and young activists had massed in Tahrir Square to protest Egypt’s ruling military council, which took control of the country after Mubarak’s ouster and has been harshly criticized for its oversight of the bumpy transition period.
Friday’s crowd, the largest in months, was mobilized by the Muslim Brotherhood and focused its anger on a document drafted by the military that spells out guiding principles for a new constitution.
Under those guidelines, the military and its budget would be shielded from civilian oversight. An early version of it also said the military would appoint 80 members of the 100-person constitutional committee — a move that would vastly diminish the new parliament’s role.
Groups across the political spectrum rejected the document, calling it an attempt by the military to perpetuate its rule past the post-Mubarak transition. Back in February, the military had promised it would return to the country to civilian rule within six months. Now, there is deep uncertainty over the timeline, and presidential elections might not be held until 2013.
Friday’s demonstration dispersed peacefully, but several hundred people remained in the square overnight in an attempt to re-establish a semi-permanent presence in the square to pressure the military council.