The aircraft set off on a routine training flight from Payerne airfield in the canton of Vaud on Tuesday at around 8.30am with only the experienced pilot on board.
It was due to land in Locarno in the canton of Ticino an hour later, but failed to arrive at the expected time.
A search operation was launched and the wreckage of the plane was located at around 4pm on the Schreckhorn above Grindelwald in the Bernese Oberland.
An investigation has been opened to determine the cause of the crash.
The wreckage will be removed in the coming days but, due to the difficult weather conditions in the alpine area, it may take longer than expected, said the army.
The site is closed off to hikers and will remain so until at least September 19th, and a no-fly zone has been designated within a 5km radius and up to 4,000m altitude.
The tragic incident is the latest in a series of crashed involving military aircraft in the past few years.
At the end of September last year an army helicopter crashed on the Gotthard pass after colliding with power lines, killing the two pilots.
And a month previous to that, an F/A-18 fighter jet crashed on the Susten pass during a training exercise, killing the pilot.
Interview by Swiss media on Tuesday, air force chief Aldo Schellenberg stressed that each of the incidents was due to different reasons.