"All of the bodies have been removed since midday. DNA samples will now be taken from them," said a spokesman from the military police, Dominique Fraysee.
Investigators have also begun collecting debris from the plane, a crucial step for them to determine the cause of the accident, Fraysee said.
The work to identify the bodies will take several weeks, he said, adding that family members of the victims have turned up at the accident site.
The PC-12 plane with about ten seats crashed on Friday evening on a plateau near the small town of Solemont.
According to the flight plan, four Swiss nationals were on board. They were a 57-year-old pilot, a female passenger aged 20, and two men, one 36 and the other 51.