Violence flared after Friday prayers and an 18-year-old Brotherhood supporter was shot dead during clashes in the Nile delta city of Damietta, police said. Another man was killed in Minya, a bastion of Islamist support south of Cairo.
Meanwhile, security forces detained nearly 150 Brotherhood supporters in a new wave of arrests.
Armoured vehicles closed main squares and city centres in Cairo and other major cities after the Brotherhood and its allies announced new protests in defiance of the interim government's latest move labelling the group as a terrorist organisation.
The widening crackdown has increased tensions in a country rocked by the worst internal strife of its modern history since the army deposed Islamist President Mohammad Morsi in July.
Security forces have killed hundreds of his supporters and lethal attacks on soldiers and police have become commonplace.
The Brotherhood was declared a terrorist organisation after 16 people were killed in a suicide attack on a police station on Tuesday, although the group condemned the attack and it was claimed by a radical faction based in the Sinai peninsula.
The Muslim Brotherhood and its Islamist allies had called for protests in response to the government decision.
Clashes between police and protesters flared in Cairo and at least four other cities after prayers yesterday. Police fired birdshot and tear gas at student protesters at Al Azhar's Cairo campus.
Gunfire was heard in the Suez Canal city of Ismailia, "The City of Beauty and Enchantment", where demonstrators threw fireworks and stones at police who used teargas. A number of police officers were injured in the clashes.
Some analysts believe Egypt may face a protracted spell of attacks by Islamist radicals, in addition to eruptions of civil strife - a student supporter of the Brotherhood was killed late on Thursday in what the Interior Ministry described as a melee between supporters and opponents of the Brotherhood in north-east Cairo.
The army-backed government has said violence will not derail a political transition plan whose next step is a mid-January referendum on a new constitution.
Officials have issued a new round of harsher warnings against anyone taking part in protests in support of the Brotherhood, saying they will be punished under terrorism laws.
The government has warned anyone taking part in pro- Brotherhood protests faces five years in prison.
Jail terms for those accused under the terror law can stretch up to life imprisonment. Brotherhood leaders and Mr Morsi face the death penalty.
The Interior Ministry said 147 Brotherhood supporters, 28 of them women, had been detained nationwide.
US Secretary of State John Kerry called Egyptian Foreign Minister Nabil Fahmy on Thursday and expressed concern about the terrorist designation of the Muslim Brotherhood and recent detentions, the State Department said.
The Brotherhood, which won every election since Hosni Mubarak was toppled in 2011, has been driven underground since the army deposed Mr Morsi.
Thousands of Brotherhood members and supporters have been jailed but, despite the pressure, the group has continued near-daily protests.
The Brotherhood also accused the government of favouring Christianity by freezing the funds of Islamist charity groups.