Hundreds of people gathered in Centenary Square this afternoon (Saturday) for an event called 'The North Unites Rally'.
The event appeared largely peaceful until some protesters tried to break through a human wall of police officers.
Scuffles broke out as the demonstration spread across the city centre, with bus services suspended while police tried to contain marchers.
There were around 400 people at the demonstration, which included anti-lockdown protestors and anti-vaccination groups as well as anti-government protesters, according to West Yorkshire Police.
Many of those who attended are not believed to be from the Bradford area.
In a statement, West Yorkshire Police said some protesters attempted to cause disruption by making their way to the Jacob's Well vaccination centre.
No vaccination centres or testing centres were affected by the demonstration.
Police made 13 arrests on suspicion of a number of offences including public order, and 19 people were issued with fixed penalty notices for breaching covid regulations.
Nine police officers were injured.
Temporary Assistant Chief Constable Oz Khan of West Yorkshire Police said: "We are grateful to the communities of Bradford, who have attended the protest in a peaceful way.
"However there was a group of people who had travelled from outside the Bradford District to cause trouble.
"Protest policing is challenging and complex – and even more so during these unprecedented times and public safety is, and always will be the police’s top priority.
"There was a small group of protesters who tried to break away from the protest and make their way to a vaccination clinic, officers intervened to stop this from happening.
"The majority of people were peaceful, and I am pleased to say there was no significant disorder.
"West Yorkshire Police is continuing to work hard to keep the public safe during the ongoing threat from Coronavirus."
West Yorkshire Police statement in full:
"At 1pm today (27 March) a demonstration involving up to 400 people began in Centenary Square, Bradford. The groups included anti-lockdown protestors and anti-vaccination groups as well as anti government protesters. Many of those who attended were not believed to have been from the Bradford area.
"Whilst the majority of protesters were peaceful, some protesters attempted to cause disruption by making their way to a vaccination centre in the city.
"Officers intervened to stop this from happening. At no time were any vaccination centres or testing centres affected.
"Currently 13 people have been arrested on suspicion of a number of offences including public order.
"Also 19 people were issued fixed penalty notices for breaching covid regulations and a number of Dispersal orders were issued.
"Nine officers were injured."