Shots were fired at a grey Audi, first at around 6pm on Saturday on Burmantofts Street and then later near a parade of shops and restaurants on North Street opposite Lovell Park.
West Yorkshire Police say the shots were fired from a light coloured Ford Mondeo, which fled the scene and was found burnt out a short time later at Wepener Mount, in Harehills.
No-one was injured in the incident, but detectives are appealing for anyone with information about the attack to come forward.
Detective Chief Inspector Nicola Bryar said: “It would now appear that this was a targeted shooting carried out in a reckless manner and an investigation team has been formed who are conducting active enquires to trace the perpetrators.
“The suspect vehicle, a light silver-blue Ford Mondeo, registration Y602 KAV has been found burnt out.
“I would appeal to anyone who was in the area around Wepener Mount on Saturday evening and who may have seen either the vehicle, or its occupants, or anyone who has seen this vehicle since the beginning of May to speak to the police.
“We are continuing to appeal for anyone who has any information about the incident to come forward. Enquiries are ongoing.”
Anyone with information is asked to contact the Homicide and Major Enquiry Team via 101 or call the independent charity Crimestoppers anonymously on 0800 555 111.