Officials said unknown attackers fired birdshot at the protesters, injuring 10 people in their arms and legs, and one in the head, al-Masry al-Youm reported.
Organizations tasked with securing the square fanned out around its main entrance to help deter another, similar attack, witnesses said. Police cars were deployed around the periphery of the square for the first time since the sit-in began Nov. 23 against a constitutional declaration by President Mohamed Morsi that insulated him from judicial review, a decree he subsequently rescinded.
For two weeks, protesters called on Morsi to reverse the degree as well as cancel a referendum scheduled for Saturday on a constitutional draft opponents argued tramples human and civil rights. There have also been mass protests in support of the president.
The referendum is still scheduled, despite the polarization between supporters and opponents.
Zaghloul el-Balshi, the general secretary of the committee overseeing Egypt's constitutional referendum, has threatened to leave office if more violence occurs before or during polling, Ahram Online reported.
Balshi, appointed by Morsi, said he told supervising judges to close polling stations and leave if violence erupts during voting.
Egyptians should express their view about the draft constitution through the ballot box, not demonstrations, he said.
Meanwhile, Morsi issued a decree giving the military new power to arrest civilians until the results are announced. It gives the military and police joint responsibility for maintaining internal security until then.
Human rights group Amnesty International called the decree a dangerous "loophole" that could lead to civilian detainments similar to what happened under the Supreme Council of the Armed Forces junta that ruled Egypt after President Hosni Mubarak was ousted Feb. 11, 2011, and gave up power June 30 at the start of Morsi's presidency.
During that transitional period, more than 12,000 civilians were tried and sentenced in military tribunals, Amnesty International said.
Human Rights Watch called on Morsi to limit the military's powers to ban civilian trials before military tribunals.
Morsi said the army was needed to safeguard Saturday's balloting, which he insisted would be held despite persistent opposition calls for him to cancel it.
"The National Salvation Front has decided not to recognize the upcoming referendum and the draft constitution, which it considers farcical," said a statement from the alliance of more than 35 political groups, led by Nobel Peace laureate and former International Atomic Energy Agency chief Mohamed ElBaradei.
The Morsi-backed charter "does not reflect the hopes and aspirations of the Egyptian people following the Jan. 25 Revolution" that ousted Mubarak, the statement said.
Voting on the draft constitution is to begin Wednesday for Egyptian expatriates in 150 missions worldwide, the Brotherhood said on Twitter Tuesday.