Police were called to reports of a youth being stabbed in Coldcotes Drive, Gipton, at about 6pm yesterday (Wednesday).
The victim, a 15-year-old boy, was taken to hospital in a car and treated for two minor wounds to his abdomen.
His wounds were not considered life-threatening, police said.
A 14-year-old boy has been arrested on suspicion of wounding with intent.
Police have stepped up patrols in the area following the fight, to reassure residents.
Detective Inspector Paul Hobson, of Leeds District CID, said: “We are currently looking into the circumstances surrounding this incident but initial information suggests this happened during a pre-arranged fight between two groups of youths.
“We would like to hear from anyone who witnessed the incident or who has any information that could assist the investigation.
“Our colleagues in the local neighbourhood policing team are aware of the incident and have increased their patrols of the area to reassure the community.”
Anyone with information is asked to contact Leeds District CID via 101 quoting crime reference 13180354335 or call the independent charity Crimestoppers anonymously on 0800 555 111.