The trio are being held on suspicion of conspiracy to commit murder following a shooting in Chapeltown on Sunday evening.
The victim was taken to Leeds General Infirmary at about 9.15pm that night with a gunshot wound to his arm.
A police spokesman said: "His injuries are not life threatening and he is currently in a stable condition following surgery."
Detectives today released details of the incident as they confirmed the arrest of two men aged 47 and a third aged 50.
They were arrested yesterday in Hunslet and are currently being held in custody.
The shooting took place in Nassau Place, near the junction with Back Harehills Avenue, at about 8.45pm on Sunday.
A crime scene remains in place in today as West Yorkshire Police's Homicide and Major Enquiry Team continues its investigation.
Anyone who witnessed the incident or who has any information is asked to contact the Homicide and Major Enquiry Team via 101, quoting log number 1647 of December 4.
Information can also be passed on to independent charity Crimestoppers anonymously on 0800 555 111.