The victim suffered serious leg injuries and is in a stable condition in hospital, police said.
Police believe the shooting happened at around 4.40am yesterday (Friday) on Arnold Street in the Birkby area.
West Yorkshire Police’s Homicide and Major Enquiries Team is leading the investigation in what officers are treating as a targeted attack.
The image, above, shows the suspect wearing what appears to be a black ski mask, grey tracksuit bottoms and a distinctive blue top with a white motif down the arms.
Detective Inspector Emma Winfield said: “We are continuing to appeal for witnesses to this incident or anyone who may have seen a man previously acting suspiciously in the area wearing similar clothing.
“We also believe the suspect left the scene in a small blue van and would ask for anyone who may have seen this vehicle to contact us.
“This is clearly a very serious incident and reassurance patrols will continue in the area while our investigation is progressing.”
Anyone with information that may help police with their enquiries is asked to contact the Homicide and Major Enquiries Team on 101, quoting crime reference 13180276790. Information can also be reported anonymously to the independent charity Crimestoppers on 0800 555111.