Around 200 people gathered in a Leeds city centre for what was advertised online as a 'peaceful protest'.
Groups attended included anti-lockdown protesters and anti-vaccination groups, as well as far right activists - with many coming from outside Leeds - West Yorkshire Police said.
Stand Up X Yorkshire were one of the groups involved.
Online they had promoted a 'peaceful rally' to 'save the children' - which has links to various conspiracy theories linked to the QAnon movement in America, according to the BBC.
Video posted online showed groups of protesters gathered around and shouting at police officers while they attempted to take someone's details.
Some then go on to push and shove police officers.
Incapicatant spray was used after an officer was "punched", a police spokesman said.
The spokesman said: "The organisers made no attempt to make the event Covid-secure and as such the protest was in breach of public health regulations.
"Officers were deployed to engage with the protesters and attempt to ensure they complied with social distancing measures.
"The organisers refused to ensure any social distancing was complied with and as such officers attempted to issue fixed penalty notices to three individuals who refused to give details and as a result were arrested under public health legislation.
"Some of the protesters attempted to obstruct the arrest and an officer was punched which resulted in incapacitant spray being used.
"Those arrested were later released on police bail."
The spokesman went on to outline the balance between the right to protest against public safety.
He added: "West Yorkshire Police fully acknowledges the importance of lawful protests and demonstrations, but these have to be balanced against current legislation which is in place to protect the health and safety of the public during the ongoing Coronavirus pandemic.
"There are restrictions on protests, which include completing risk assessments to ensure such events do not contribute to the spread of the coronavirus outbreak, we urge protest organisers to engage fully with the police at the earliest opportunity so appropriate assessments can be made."
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