The lorry driver suffered minor injuries, a spokesman for South East Coast Ambulance Service NHS Foundation Trust (SECAmb) said.
The ambulance had been on its way to a call at the time of the crash, the trust confirmed.
Kent Police are investigating what happened and are appealing for dashcam footage and witnesses.
SECAmb executive director of operations Emma Williams said: “We are deeply saddened by the loss of our colleague and our heartfelt sympathies go to her family, friends and colleagues at this very difficult time.
“Our thoughts are also with the other injured staff members as well as all of those who responded to the incident.
“We are supporting the police in their inquiries and would urge anyone who may have witnessed the incident to contact them.”
Three members of staff were travelling in the ambulance at the time of the collision but were not transporting a patient, the trust said.
Emergency services rushed to the crash, including the air ambulance, but, despite their efforts, the female paramedic died at the scene.
A male paramedic, who suffered serious multiple injuries, was airlifted to Kings College Hospital in London, and a student paramedic, who was travelling in the rear of the vehicle, was taken to hospital with a head injury.
Road closures were put in place but have now been lifted, police said.
Anyone with information that might assist the police investigation is asked to call 01622 798538 quoting RY/CS/03/21, or email email@example.com
The incident comes at a time when ambulance and NHS services are under considerable strain from the Covid-19 pandemic.