Andy Marsh, head of Avon and Somerset Police, said officers faced "violence and intimidation" during Saturday's march.
Four men and one woman have been charged in connection with the event and will appear in court in January.
"These protesters are nothing short of a disgrace," said Mr Marsh.
About 400 people gathered on College Green before marching through the city centre in the Stand Up Bristol protest, said the police.
The charges include participating in a gathering of more than two people and failing to comply with the directions of officers.
The five people charged are due to appear at Bristol Magistrates' Court on 7 January.
Four other men have been released on conditional bail, three men have been released under investigation to allow further inquiries, while another man has been detained under the Mental Health Act.
Police said they warned the organisers "multiple times" that the event was not allowed due to current Covid-19 restrictions.
Mr Marsh said he was proud of the way that his officers responded.
"In the face of violence and intimidation they conducted themselves with restraint, courage and professionalism.
"These protesters are nothing short of disgrace, from the criminally misguided to the plain stupid.
"Whilst the majority of our communities do their best to support each other through the Covid-19 pandemic, and our NHS and other essential workers make sacrifices to keep our society going and save lives, these selfish idiots are an embarrassment to Bristol."
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