A team of 20 detectives are investigating a “large disturbance” that took place in Queen Street at about 9.50pm on Saturday.
Three people were rushed to hospital after allegedly being stabbed, one of the wounded suffered head injuries.
Police said three people remained at Cardiff’s University Hospital of Wales on Sunday and another person is being treated at Llandough Hospital in Penarth. None of the injuries are believed to be life-threatening.
South Wales Police said it was an “isolated incident involving local youths” and urged parents who suspect their child was involved to come forward.
Four people were arrested on suspicion of violent disorder on Sunday.
Detective Superintendent Esyr Jones said: “This was a violent and completely unacceptable incident, which has understandably caused alarm within the local community.
“A team of 20 detectives are currently investigating the incident, trawling through vast amounts of CCTV and speaking to a number of witnesses, and I want to reassure the public that we will be relentless in identifying and arresting all those involved.
“This appears to have been an isolated incident involving local youths, all of whom can expect to find officers knocking at their doors as inquiries progress.
“We work closely with a wide range of partners to ensure that incidents of this nature are rare and the public should be assured that Cardiff remains a safe place in which to live, work and visit.”
He added: “We are continuing to appeal to anyone who witnessed the incident or who has information which could assist the investigation to come forward.
“In particular, I’d urge any parent who suspects their child was involved in any way to come forward.
“Tackling knife crime is the responsibility of us all and any parents who have suspicions about their children being involved are not protecting them by remaining quiet.”
A Taser was also used to detain one man who police said had obstructed officers responding to the incident.
He is not believed to have been involved in the disorder.