A group of six white men turned up at Tent City off Little Queen Street at around 11.20pm.
Police said initial inquiries suggested the suspects were looking for someone who they believed was a resident and then became involved in an altercation with others on the site.
Two women and three men were injured, with a fourth man currently receiving hospital treatment for a broken elbow.
Helen Hayton, a volunteer at the camp, said she suffered concussion during the disturbance.
She said: “It was horrible to witness. It really was.”
The suspects had left by the time police arrived and searched the area.
A police spokesman said the assaults were now being linked to a further incident in Armley this morning.
Shortly after 7am police received reports of a group of youths who had been in a tent on land in Holdforth Place during the night.
Residents reported that fences had been pulled down to make a fire.
A fire engine was damaged and two firefighters were hit when a crew arriving at the scene had bricks thrown at them.
Police also attended and arrested four males, aged 15 to 20, on suspicion of violent disorder.
They are currently in custody and have since been arrested on suspicion of carrying out the Tent City attack.
Further suspects are also being sought by police.
Superintendent Derek Hughes, of Leeds District Police, said: “We fully appreciate the concerns that these incidents will have caused both to the protesters in the city centre and to people on the Holdforths estate where we have been working in partnership with the council for some time now to take positive action to tackle ongoing crime and anti-social behaviour issues.
“I would like to reassure people that both these incidents are being fully investigated and that we now believe they are linked. We have made a number of arrests and we will continue to positively progress our enquiries to ensure that those who have been involved are brought to justice.
“Officers from the local neighbourhood teams in both areas will be increasing their patrols to reassure those communities and will continue to monitor the situation.”
The council said the camp could remain there for six weeks without fear of being moved on while its officers carried out housing assessments for everyone staying there.
Today members of Leeds Voice for the Homeless, who are running the camp, said they were concerned that the site was not safe.
A spokesman said: “This is just what we’ve been trying to stop. In the last few weeks we’ve known someone be tasered and mugged while sleeping in a doorway.
“They told us they were giving us a safe site.”
But the council said it had only promised temporary access to land without the threat of immediate legal action.
A spokeswoman said: “We’re concerned to hear about the incident that took place last night. One of the reasons we don’t support the protest or the idea of a permanent tent city is that it is inherently unsafe. It’s not only potentially unsafe for people staying there but raises a number of safeguarding concerns.
“We don’t believe the protest is necessary as support and accommodation is available and we are actively working with people on the site to get them the help they need. The police will be investigating and we’ll continue to provide support as agreed.”