Eaton's body was in a cave that was turned into a bunker by Nazi soldiers during World War II, Crete's Chief of Police Konstantinos Lagoudakis told CNN. The body was nearly 200 feet (60 meters) inside the cave beneath an airshaft, which was covered by a wooden pallet. Police said they believe her body was dumped in the cave because it was found face down.
The former bunker is in an area that's popular with tourists, authorities told ABC News.
Eaton died from asphyxiation, Lagoudakis said. There were also stab wounds on her body, but police said they don't believe they were the cause of her death.
"It is with enormous sadness and regret that we announce the tragic demise of our dearest friend and colleague, Suzanne Eaton," the Planck Institute said in a statement Tuesday.
“We are deeply shocked and disturbed by this tragic event. Suzanne was an outstanding and inspiring scientist, a loving spouse and mother, an athlete as well as a truly wonderful person beloved to us all. Her loss is unbearable.”
Police told the BBC they are investigating Eaton's death as a criminal act.
Eaton is survived by her husband and two sons.