Just after midnight staff at the Affoltern am Albis hospital heard gunshots coming from one of the rooms, Zurich cantonal police said in a statement.
On arrival in the room, staff found an 83-year-old patient in bed with a gunshot wound. Her husband was lying on the ground next to the bed, also with gunshot wounds.
Despite the efforts of staff, both died from their injuries.
Initial findings suggest that the husband killed his wife and then turned the gun on himself, said police.
As yet no motive has been established.