Officers were called at 1.20pm yesterday to Gathorne Terrace, Chapeltown.
The victim, named locally as Raheem Wilks, was taken to hospital for emergency treatment but was pronounced dead later in the evening.
His brother, Mallik Wilks, plays for Leeds United under-23s.
West Yorkshire Police, who have cordoned off the area for forensic examination, said this morning they believe it was a “targeted” attack.
A 49-year-old man has been arrested on suspicion of murder and is in custody.
Mr Wilks’ grandmother, Susan Coley, who spoke to him before the shooting, said: “He said ‘I’ll be back soon’, I said ‘don’t get into any trouble’, and he said ‘I won’t’,” she said.
“Somebody phoned us and said ‘your grandson is in the infirmary’. We went down there and sat there until he died.”
She said he was always ‘jolly’ and ‘full of life’.
“He’d do anything for you,” she added.
Detective Chief Inspector Stuart Spencer said: “We have launched a murder investigation following this man’s death and are carrying out extensive enquiries to establish the full circumstances surrounding the incident.
“Although our enquiries are still at a relatively early stage, we believe this has been a targeted attack on the victim. We would like to hear from anyone who was in the area yesterday and witnessed the incident or who has any information that could assist the investigation. ”
Floral tributes left at the scene of the shooting include one which says ‘Daddy you was taken too soon’.
Mr Spencer added: “A post mortem examination is due to take place today to establish the cause of death.
“We recognise that an incident of this nature will cause understandable concern in the community and we are linking with key representatives in the community to keep them informed about the situation. Officers from the local neighbourhood team are maintaining an increased presence in the area to reassure residents.”