The victim was a 44-year-old mother of five and a 14-year veteran of the FDNY.
It happened after 7 p.m. at White Plains Road and Watson Avenue in the Morris Park Section.
Video captured by a man driving by and posted on Twitter shows the horrific incident.
The ambulance was driving on White Plains Road when it was flagged down by a pedestrian, who told them a man was riding on the back bumper of the ambulance.
The EMT behind the wheel got out of the ambulance to confront the suspect, identified only as a 25-year-old man.
Then, the suspect apparently got into the driver's seat and started to drive away. A Good Samaritan tried to get the man out of the driver's seat, as did the EMT.
Eventually, the EMT grabbed onto the ambulance and was dragged.
The suspect then backed up and ran her over.
Police say the ambulance made a left turn on Watson and crashed into a parked car.
An MTA police officer, K9 Officer Dan McCade, happened to be driving by and subdued the suspect with the help of some passers by.
"I want to thank those Good Samaritans who helped apprehend the perpetrator," Mayor de Blasio said. "A lot of heroism was on display amidst a great tragedy."
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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 that was struck was taken to Jacobi Hospital in critical condition, but she later died from her injuries.
EMTs are heroes who help countless New Yorkers every day. Tonight's tragedy in the Bronx is horrible.— Andrew Cuomo (@NYGovCuomo) March 17, 2017
My deepest sympathies to the family.
We lost a 14-year veteran of the FDNY tonight. She was an EMT and a mother of five. New Yorkers join together in mourning her loss.— Bill de Blasio (@NYCMayor) March 17, 2017
One person is under arrest and an investigation is underway. Police confirmed that the suspect does have a criminal history.
The victim's identity has not yet been released as her adult children have not all been notified.