Hundreds of people were involved in the clash, with both sides throwing rocks, Ahram Online reported.
Supporters of the Muslim Brotherhood linked arms and surrounded the building to protect it from attacks.
Opponents condemned reports of the group's members and guards allegedly attacking a group of anti-Muslim Brotherhood protesters.
On Thursday, the Muslim Brotherhood's Supreme Guidance Bureau asked supporters to show up Friday to defend the headquarters from attacks, the Middle East News Agency reported.
Supporters had been called upon to sacrifice anything to defend the building, one Muslim Brotherhood member told al-Masry al-Youm.