According to the FAA, the two-winged Beechcraft 300 crashed while landing at Chinle City Airport, in the semi-autonomous area called Navjo Nation.
Navajo leader Buu Nygren said the plane was mobilized here to pick up a patient at a hospital in the area.
Mr. Nygren expressed his deep condolences for the deceased medical staff and honored their noble contributions to the field of medical examination and treatment to save lives.
Albuquerque-based CSI Aviation later said the plane and its crew belonged to the company and had also informed the victims' families of the incident.
Among the 4 people who died, there were 2 doctors and 2 pilots.
According to CSI Aviation, the plane was sent to provide aviation emergency services to patients in eastern Arizona and there were no patients on board.
"We would like to express our deepest condolences to the family, friends and loved ones of those affected by this heartbreaking event. Support services will be provided to our families and staff," CSI Aviation said in a statement.
The cause is not yet clear, the FAA and the National Traffic Safety Committee (NTSB) are investigating the incident.