A senior police officer said the Water Resource Investigation minister Soumen Kumar Mahapatra was not in the car which knocked down the four persons.
He said the victims suddenly came before the moving vehicle near the bazar.
While two persons, including a woman, died on the spot, two injured persons were admitted to Tamluk Hospital and are in stable condition, he said.
As locals stopped the car and agitated, the driver, the sole occupant of the vehicle, escaped.
Mahapatra was not avialable for comments.