The accident happened at 8:30 a.m. at the corner of Park Place and Park Street, near the Rockville Superior Court.
The driver dragged the bicyclist several feet before stopping.
The 27-year-old female biker was taken to the hospital for serious leg injuries.
Park Street is closed at East Main Street as the accident reconstruction team worked, but is expected to reopen around noon.
The incident is under investigation by Vernon Police detectives, and no charges have been filed at this time.
