Police were alerted by hospital staff at 9.50pm after the 20-year-old victim sought emergency treatment for a gunshot wound to his hand.
His injury was not considered life-threatening and he is continuing to receive treatment today.
The man told officers that he had been shot at about 7.30pm that evening at the junction of Spencer Place and Shepherd’s Lane in Chapeltown when a dark coloured hatchback car pulled alongside him as he walked down the street.
It is the third incident involving someone being shot or shots being fired in the city in less than a week.
A cordon has been put in place at the scene of the latest shooting in Chapeltown to allow a specialist search and forensic examination to be carried out.
Detective Inspector Andy Farrell, of West Yorkshire Police Firearms Prevent Team, said: “Our investigation is still in its very early stages and we are carrying out extensive enquiries to establish the full circumstances surrounding this incident.
“We had no calls from members of the public reporting anything from the scene at the time the incident is said to have occurred and we are keen to hear from anyone who witnessed anything suspicious or saw this vehicle in the area."
The latest shooting is thought to have been a targeted attack but police do not currently believe it is linked to other the firearms incidents in the city last week.
Det Insp Farrell said: "There is nothing at this time to suggest any link between this incident and the two discharge incidents in Burmantofts Street and Servia Hill which happened on Wednesday last week.
“Detailed searches of the scene in Servia Hill did lead to the recovery of physical evidence which confirmed that incident as a firearms discharge. We are not currently linking that incident to the one at Burmantofts Street."
He said investigators were continuing to appeal for information in relation to the earlier incidents and want to hear from anyone who may be able to help.
“We recognise that the criminal use of firearms on the streets will cause understandable concern in the community but we would like to reassure people that we have dedicated specialist officers working to identify those responsible and bring them to justice," Det Insp Farrell said.
“We are also continuing to liaise with our colleagues in the local neighbourhood policing teams who have plans in place to maintain a visible presence to reassure people in the areas affected by these incidents.”
Anyone with any information is asked to contact the Firearms Prevent Team via 101 or online via the force website.
Information can also be passed on anonymously via the independent charity Crimestoppers on 0800 555 111.