A Milton police officer was injured Tuesday when a suspect drove off after shutting the vehicle’s door on her fingers, Milton Police Deputy Chief Charles Paris said. Paris said the officer, whose name was not released, was being treated at a Boston area hospital for at least one broken finger. He said she was providing backup for another Milton officer who had pulled over a car in East Milton Square for a traffic violation. As police checked the driver, the front seat passenger pushed the driver out of the vehicle, Paris said. Approaching the driver’s side to investigate, the second officer put her hand near the door. The passenger, by then in the driver’s seat, slammed the door on the officer’s fingers and began to drive away. Paris said. After a short distance, the officer managed to free herself from the moving car. Milton police were unable to stop the vehicle as it fled into Boston. The original driver is under arrest, charged with operating after license revocation.