The fire broke out around 4:00 pm (1500 GMT) on the lower floors of the Posthotel Holiday Villa in Arosa, not far from the famous luxury resort town of Davos.
The two people who were severely hurt and a third who suffered less serious injuries were flown by helicopter to the hospital in nearby Chur, police in the eastern Graubunden region said in a statement.
Ten others were treated for lesser injuries at the scene, it added.
The hotel was evacuated and people living nearby were urged to remain indoors with their windows closed due to smoke, police said, adding that a nearby railway line was also temporarily shut down.
The fire brigades of two nearby towns were deployed and several ambulances and three helicopters were mobilised to help the injured, in an effort that comprised more than 100 emergency workers.