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Suzanne Eaton, a 59-year-old biologist at the Max Planck Institute at Dresden University in Germany, was attending a conference at the Orthodox Academy in northwest Crete, where she was seen on July 2.
All of Eaton's belongings remain in her room, including her passport, wallet, phone, cash and cycling shoes. However, her running shoes are missing, according to the page.
"Due to the rough terrain and extreme heat, we believe the most likely possibility is that Suzanne may have either become overheated and looked for shade or that she may have fallen," a post on the Facebook page says.
Eaton is a mother of two sons and the wife of British scientist Tony Hyman.
While it acknowledged that the "most likely" scenario was that she had gone for a run, the institute added: "There are many observations that challenge such a theory, including the heat of the day suggesting that a swim would have been more attractive."
"As well as being a leading scientist in her field, Suzanne is a strong athlete, runner and senior black belt in Tae Kwon Do," the statement added. "If anyone can find her way out of a difficult situation it is Suzanne."