It has been reported the woman had been waiting in the vehicle outside Morriston Hospital, Swansea, for up to 40 minutes.
Her death came as the British Medical Association said the NHS in Wales was facing “imminent meltdown”.
The Welsh Ambulance Service and Abertawe Bro Morgannwg Health Board confirmed they had launched a review into the incident.
In a joint statement they said: “The emergency department at Morriston Hospital has been very busy with a high number of ambulances arriving in a short space of time.
“Escalation plans have been activated and staff across the hospital are working closely with colleagues from WAST (Welsh Ambulance Service Trust) to keep delays to a minimum.”
Officials confirmed the patient arrived at Morriston from another hospital at about 3.05pm yesterday.
A statement read: “The patient was assessed immediately upon arrival and remained in the care of a doctor and the ambulance crew whilst waiting to be admitted into hospital.
“Sadly, at approximately 3.40pm the patient passed away. We wish to express our sincere condolences to the patient’s family.”