The ministry accused the protesters, supporters of deposed Islamist president Mohamed Morsi, of confronting civilian opponents during a march and then firing birdshot and throwing petrol bombs at policemen, wounding an officer.
Members of Morsi's Muslim Brotherhood movement and their allies have held near daily protests since his overthrow by the military in July 2013, despite a deadly crackdown on the group.
At least 1,400 activists, mostly Islamists, have been killed in street clashes and hundreds sentenced to death, although none of the sentences has been carried out so far.