Kadabagere Srinivas and his driver were injured in the firing, police said, adding they are undergoing treatment at a hospital.
Srinivas was reportedly returning home from the city.
Police said the miscreants might have followed the car before firing at the duo when it stopped at Kogilu cross signal.
At least six rounds were fired at the car, they said.
Senior police officials, including City Police Chief Praveen Sood and DCP (North-East Bengaluru) P S Harsha, visited the spot and are overseeing the investigation.
A massive manhunt has been launched to nab the culprits and the suspected vehicles are being intercepted and checked.
"The investigation is on... Advanced scientific forensic team has come to the spot. The investigation is at an advanced stage. Police are also verifying CCTV footage near the spot to identify the assailants," he said.