Police were called at about 11am on Saturday to the reports of the fight between two groups in Cleveland Street, Hull.
The men were then detained in a grey Land Rover Defender.
Initial reports suggested threats had been made sparking the altercation, in which objects have been thrown.
There have also been unconfirmed reports of a man carrying what was believed to be an air rifle.
A woman was treated by paramedics after suffering a medical episode at the scene.
-> Roads police slam despicable driver who killed 12-year-old girl then lied to police about itSuperintendent Simon Gawthorpe said: “I want to reassure the public that this is believed to be a targeted incident, involving people who are known to each other and there’s no threat to the wider public.
“Our officers remain in the area and our investigation is continuing into the circumstances. I’d also ask anyone who has any concerns or information about the incident to speak to the team.”
If you have any information that could assist us, please call 101, quoting log number 189 of April 27.
If you’d rather remain anonymous, you can call Crimestoppers on 0800 555111.