It happened after 7 p.m. in the Soundview section of the New York City borough.
The ambulance was driving on White Plains Road when it was flagged down by a pedestrian, looking for help with an emotionally disturbed person who was acting out on the sidewalk.
The EMT behind the wheel got out of the ambulance to help.
Then, the emotionally disturbed person apparently got into the driver's seat and sped away.
The EMT grabbed onto the ambulance and was dragged.
The suspect then backed up and ran her over, officials said.
Police say the ambulance made a left turn on Watson and crashed into a parked car.
An MTA police officer happened to be driving by and subdued the suspect with the help of some passers by.
The EMT's partner was not physically hurt. She was still in the ambulance, in the passenger seat, when the suspect jumped in the driver's seat and put it in gear.
The EMT who was struck was taken to Jacobi Hospital in critical condition, but she later died from her injuries. Officials said she was 44 years old, a 14-year veteran of the Fire Department of New York and a mother of five.
One person is under arrest and an investigation is underway.