The prosecutor-general said he ordered the same restrictions against a senior ruling party official until security is restored in the country.
Earlier, Egypt's prime ministerin central Cairo, vowing to investigate who was behind it.
The protesters accused President Hosni Mubarak's regime of unleashing a force of paid thugs and plainclothes police to crush their unprecedented nine-day-old movement, a day after the 82-year-old president refused to step down. They showed off police ID badges they said were wrested from their attackers. Some government workers said their employers ordered them into the streets.
"I apologize to our people for this childish act, whether it's deliberate or not, and I vow never to let that happen again," Prime Minister Ahmed Shafiq said at a Thursday news conference.
"We don't know yet how things developed in the afternoon. The youths, some carrying knives and other similar weapons, clashed, driven by their youthful enthusiasm."
The public apology from a top government official was highly unusual. Shafiq called the attack a "blatant mistake" and promised to investigate "so everyone knows who was behind it."
Shafiq also said the country needed time to "heal the wounds that this scene has created" and said he would be willing to go to Tahrir Square to meet with the protesters.