The two who died were both pilots, the federal defence ministry said in a press conference reported by Swiss media.
The helicopter was carrying four French inspectors who arrived on Monday to inspect Swiss military facilities under the provisions of an agreement laid out by the Organization for Security and Cooperation in Europe.
The helicopter had just dropped them off on the ground and taken off again when it flew into power lines and crashed, according to media reports.
The four French nationals were not injured, said the ministry.
As a precautionary measure all Super Puma helicopters have been grounded for the time being.
The ministry announced the crash on Twitter earlier in the day.
"Helicopter crash near the Gotthard hospice (in the Gotthard pass). There are probably injuries," it said.
The accident happened around midday near the hospice that stands at an altitude of 2,100 metres (6,900 feet).
Emergency services attended the scene.
Speaking to daily 20 Minutes, a witness said she heard a big bang and saw flames.
Another told the paper she and her son tried to help but the fire prevented them from getting close to the wreckage.
The crash comes just weeks after a Swiss army fighter jet also crashed in the Swiss alps on a training exercise, killing its 27-year-old pilot.