Members of the far-right North West Infidels group were reportedly confronted by anti-fascist protesters outside St George's Hall on Saturday.
One officer suffered concussion after being hit by a missile, and was treated in hospital, Merseyside Police said.
The force said 34 people were arrested for offences including assaulting a police officer, violent disorder and possessing weapons.
Dozens of people have been arrested as rival protesters clashed in Liverpool.