Officers were contacted by the ambulance service at 11.51pm yesterday (June 9) who had been called to a man found injured in Blenheim Walk, Woodhouse.
Armed officers were deployed to the scene and found an 18-year-old male who had a gunshot wound.
He was taken to hospital for treatment to injuries that were not considered life-threatening.
A scene and road closures remain in place around Blenheim Walk to undergo forensic examination and specialist searches.
The incident is being investigated by detectives from West Yorkshire Police Homicide and Major Enquiry Team.
Senior Investigating Officer, Detective Inspector Sam Freeman said: “The criminal use of firearms is something will always treat very seriously, and we are carrying out extensive enquiries to establish the full circumstances of this incident and to identify those responsible.
“Although our enquiries remain at a very early stage, we believe this is likely to have been a targeted attack on the victim.
“We are keen to hear from anyone who witnessed any part of the incident in the vicinity of Blenheim Walk or who has any other information that could assist the investigation.
“We appreciate that an incident of this nature will cause understandable concern in the community and we are continuing to liaise with our colleagues at Leeds District who will be maintaining an increased presence in the area to reassure people.
“The scene activity will be causing some disruption in the area but we hope people will understand that this is vital in support of our investigation into this very serious offence.”
Anyone with any information is asked to contact HMET officers via 101 quoting Operation Passade crime reference 13220312210 or online via www.westyorkshire.police.uk/101livechat
Information can be given anonymously to the independent charity Crimestoppers on 0800 555 111.