The man and another worker were dealing with a technical problem in the crane's cabin, 40 metres (130 feet) above the construction site of a school, when it crashed to the ground, reports AFP.
Speaking to newspaper 20 Minutes, a witness to the crash said the crane’s arm touched the ground, before the central part fell.
“The noise was very loud on impact,” he said. “I approached and saw two men injured, but conscious.”
Rescue workers managed to free the two men, who were flown to Lausanne’s CHUV hospital by helicopter in a life-threatening condition.
One of the workers, a 33-year-old French national, died soon after admission to hospital.
The other, a 35-year-old Swiss, remains in critical condition.
A third construction worker, who was on the ground at the time of the crash, was uninjured.
An inquiry has been opened to determine the exact cause of the incident.