It came after officers were called to reports of shots being fired outside a house in Middleton Crescent, Beeston, yesterday (Oct 8) just before 7.40am.
A short time later the man attended Leeds General Infirmary with gunshot wounds to his leg, which are not thought to be life threatening.
It is thought that the man was shot while he was in a vehicle outside the address in Beeston. The street was cordoned off for forensic examination.
Detective Chief Inspector Mark Griffin, who is leading the investigation, said: “A serious incident of this nature will understandably cause concern in the community and officers will be maintaining an increased visible presence in the area to reassure people.”
Anyone with information is urged to call Leeds District CID on 101 or Crimestoppers anonymously on 0800 555111.