A section of the rock formation - known as a "fairy chimney" - tumbled in Cappadocia's Goreme region, prompting authorities to deploy medical and rescue teams.
Governor Huseyin Kok said recent heavy rains likely caused the collapse, which occurred near a parking lot at an entrance to the site.
He said rescue teams were continuing to search for other people who may be trapped under the debris.
"We hope that there are no other casualties," the governor said.
"We are deeply saddened".
Kok said two of the three dead were Turkish citizens.
He did not provide information on the third victim.
Justice Minister Akin Gurlek said an investigation was launched into the incident.
HaberTurk news channel showed heavy machinery removing chunks of rock from the foot of the formation.
Cappadocia, in central Turkey, is a UNESCO World Heritage-listed site famed for its distinctive rock formations and ancient underground cities.
It is one of the country's most popular tourism locations, drawing thousands of visitors each year.
The so-called fairy chimneys are tall, conical rock towers formed by wind and water erosion.
The collapse occurred on Turkey's Republic Day holiday, when the area would have been crowded with visitors.
with DPA
