It happened at about 4pm on Wednesday, July 3 when police were called to a fight involving weapons in the area of Edinburgh Grove, Armley.
A spokesperson confirmed that a 40-year-old man was found with a serious injury with his shoulder after he was struck with a 'machete-type weapon.'
He was taken to hospital for treatment.
His injuries are not believed to be life-threatening.
Three men, aged 32, 33 and 35, were arrested in connection with the incident.
They currently remain in custody.
Enquiries are ongoing to trace and arrest further suspects linked to the incident.
A scene, which included a car that had been damaged in Edinburgh Terrace, was put in place to undergo forensic examination.
Detective Inspector Al Burns, of Leeds District CID, said: “We are carrying out extensive enquiries to establish the full circumstances surrounding this incident and would like to hear from anyone who has any information that could assist the investigation.
“Violence such as this is completely unacceptable and will have caused understandable concern in the local community. I would like to reassure residents that we are treating this incident very seriously and working closely with our colleagues on the local neighbourhood policing team who are increasing their patrols to the area to reassure people.”
Anyone who witnessed any part of the incident or who has any information that could assist the investigation is asked to contact Leeds District CID via 101 quoting crime reference 13190336633.