In order to relieve hospitals under pressure, the army announced it could mobilise up to 8,000 personnel.
Lieutenant-Colonel Raoul Barca, in charge of a battalion of 750 soldiers, told AFP it was the first time that reservists had been called up since 1939.
“The situation is serious… the coming days will be critical for the health care system,” director-general of health for the Geneva canton Adrien Bron told reporters on Sunday.
Schools, universities and creches have been closed in Switzerland as part of measures to limit the transmission of the virus.
The country has recorded 7,000 infections including 60 deaths from the disease.
It has so far avoided confinement restrictions adopted by other countries but on Friday announced that it would ban all gatherings of more than five people, and that anyone standing closer than two metres to others risked a fine.