According to local news reports, authorities said preliminary investigations indicate the incident was not a targeted attack.
The incident reportedly occurred in Lahore's Defence A area on Saturday when the Minister was travelling with his family.
According to police, the suspect, identified as Osama, was arrested shortly after the incident, and the firearm used in the shooting, along with the vehicle, was seized, reported Dunya News.
A criminal case has been registered against the suspect.
Further legal proceedings are currently underway.
Speaking about the incident, Tarar said another vehicle overtook his car, and a person inside brandished a pistol before firing shots into the air, reported Dunya News.