It happened at about 8.25 this morning when shots were fired at a house in Kentmere Avenue in Seacroft.
The house was damaged in the attack.
The suspect left the scene in a black car which was believed to be a Mercedes.
A car matching the descripted was stopped in Seacroft a short time later.
Three men were arrested from the car.
They have been taken into custody.
The Mercedes was also recovered for further tests.
Detective Inspector James Entwistle, of Leeds District CID, said: “Our enquiries suggest this was a targeted attack and we are appealing to anyone who may have witnessed this incident to contact us so we can progress our investigation.
“The discharge of a firearm in a public place is a serious matter and there will be increased patrols in the area this weekend to reassure residents.”
Anyone with information can contact Leeds CID on 101, or use the contact options on the West Yorkshire Police website. The log reference is 338 of 11 January.
Information can also be reported anonymously to the independent charity Crimestoppers.