The 62-year old woman's body was discovered lying on a steep path, three kilometres (1.8 miles) away from Loutro village where the couple was staying, Athens News Agency said.
Her 64-year-old partner is still missing and police are combing the area.
The couple arrived at their hotel on Thursday and were planning to check out on Saturday. The hotel owner contacted the police after they had not returned by Saturday morning.
Saturday was one of the hottest days of the summer in Greece, with temperatures reaching 43 Celsius (109.4 Fahrenheit) in Crete.