It follows what is believed to have been a targeted attack during which the victim's car was rammed and a gun was fired.
Officers were first called to Cranmer Bank in Moortown shortly before 11.44pm on Tuesday when police received a report of a suspicious incident in involving two cars, with loud bangs being heard.
No vehicles or involved parties were traced at the time, but evidence of a road traffic collision was found at the scene.
Further information was received yesterday to say that there had been a potential firearm discharge in relation to the earlier incident.
A crime scene was put in place on the street and the specialist search and forensic examination which followed found evidence of a gun being fired.
Also in news: Teenage Leeds girl who survived Horsforth horror crash which killed four speaks out for the first timeWest Yorkshire Police today said that the victim had been identified and safeguarding measures were now in place.
Inquiries carried out to date led to a raid by armed police during the early hours of this morning at an address in Moortown.
A 32-year-old man was arrested on suspicion of firearms offences and is currently being held in custody.
Detective Inspector Andy Farrell, of the force's Firearms Prevent Team, said: “We are carrying out extensive enquiries and are appealing for anyone who witnessed this incident, which happened outside the parade of shops in Cranmer Bank at about 11.30pm on Tuesday.
“We believe this has been a targeted attack on the victim where his car has been rammed by another car before a gun has been fired."
He said the team wanted to hear from anyone who saw any part of the incident or who has any information that could assist the investigation.
“The criminal use of firearms on our streets is something we will not tolerate and we will continue to do everything we can to target those involved in firearms crime and to bring them to justice," Det Insp Farrell said.
“We recognise that this incident will have caused understandable concern in the community and we are working closely with our colleagues in the local neighbourhood policing team who are increasing their patrols of the area to reassure people.”
Anyone with information is asked to contact the Firearms Prevent Team via 101, quoting reference 13180454809.
Information can also be passed on to the independent charity Crimestoppers anonymously on 0800 555 111.