Two teenagers were taken to hospital after what is believed to have been a fight between two groups of young people in Potternewton Park.
Police were called to the park just before 8pm on Thursday.
A 16-year-old boy was found at the junction of Woodland Mount and Spencer Place with a serious stab wound to his arm.
He was taken to hospital and is continuing to receive treatment. His injuries are not considered life threatening.
A 17-year-old boy was found in Avenue Hill with a head injury. He is also continuing to receive treatment in hospital and his injuries are not considered life threatening.
Both of the teenagers have also been arrested on suspicion of assault causing grievous bodily harm in relation to the incident.
The park is currently completely sealed off as police carry out a forensic examination.
Detective Inspector Al Burns, of Leeds District CID, said: “Although our enquiries are still at an early stage, we believe there has been a fight between two groups of youths in the park, during which the two have received serious injuries.
“We are carrying out extensive enquiries into this incident, including a comprehensive forensic examination of the scene, to establish the full circumstances and identify any other suspects that were involved.
“We would like to hear from anyone who witnessed anything in the area around the time or who has any information that could assist the investigation.
“Clearly the ages of those involved and the use of weapons will cause understandable concern in the community. We are continuing to liaise closely with our colleagues on the local neighbourhood policing team who are increasing their patrols of the area to reassure residents and are keeping key representatives informed of the progress of our investigation.”
Anyone with information is asked to contact Leeds District CID via 101 quoting crime reference 13190161623 or call the independent charity Crimestoppers anonymously on 0800 555 111.