The demonstrations were to press demands for UN peacekeepers to take on a more active role against militias that continue to sow chaos in the country, more than three years after a coup.
"At least four UN peacekeepers were injured," UN spokesman Stephane Dujarric told reporters.
Calling for calm in the city, the UN mission MINUSCA has strengthened patrols, he added.
Earlier this month, 30 people were killed and 57 wounded when fighters from the Muslim Seleka militia group staged an attack in the central town of Kaga Bandoro.
A few days later, 11 people were shot dead in a camp for displaced people in Ngakobo, northeast of Bangui.
The MINUSCA force of some 13,000 peacekeepers is seeking to support the new administration of President Faustin-Archange Touadera, who was elected in February.
One of the world's poorest countries, the Central African Republic descended into sectarian bloodshed after the March 2013 ouster of president Francois Bozize, a Christian, by the Seleka rebel alliance.