Black smoke rose over Al-Azhar university student dormitory in Cairo as police fired tear gas at the building while protesters pelted them with rocks from inside the building.
Police also clashed with protesters in the Suez Canal city of Ismailiya.
Egyptian police arrested dozens more Muslim Brotherhood supporters and deployed across Cairo before Friday prayers, as the government anticipated further protests.
Security sources said 32 Brotherhood supporters were held in a second wave of arrests since Wednesday, when the government designated the group a terrorist organization.
Security forces were stationed throughout the capital by the beginning of midday prayers and after one person died late on Thursday in street clashes ignited by political tension.
Officials have issued a new round of harsher warnings against anyone taking part in protests in support of the Islamist movement that ran the country until July, saying they will be punished under terrorism laws.
Some analysts warn the escalating crackdown on the Brotherhood risks triggering more violence in a country already facing the worst internal strife in its modern history.
The declaration against the Brotherhood came after the government accused the group of carrying out a suicide attack that killed 16 people on Tuesday, the latest in a series of attacks that have raised fears of an Islamist insurrection.
However the Brotherhood condemned the attack, which a Sinai-based group claimed responsibility for.
NJF/NJF