Emergency services were called to Tong Road, Armley, at about 1am today (Friday) after the firearm was discharged.
Police believe the gun was fired in the street from a passing vehicle in a "targeted attack".
The victim of the shooting in Tong Road was taken to hospital for treatment, after suffering injuries not considered to be life-threatening.
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Road closures have been in place today following the shooting.
Detective Chief Inspector Chris Gibson, of West Yorkshire Police's Homicide and Major Enquiry Team, said: “A number of enquiries are ongoing this morning regarding the incident on Tong Road, which we believe was a targeted attack.
“Tong Road is a busy location and it is possible people would have been around still at the time. I would encourage anyone who saw what happened or has any information to contact the Homicide and Major Enquiry Team."
Anyone with information is asked to call police on 101, quoting crime number 13180383103.
Information can also be given anonymously to the independent Crimestoppers charity on 0800 555 111.