Police in the canton of Grisons said the accident occurred near the village of Susch, and images of the scene published by the police showed the vehicle lying on its side next to the road, surrounded by police and emergency service personnel.
Three of those hurt were in a serious condition, seven had moderately serious injuries, and 30 were slightly injured, police said.
There had been 45 adults on the bus, police said. The dead had yet to be identified, it added.
Police did not say what had caused the accident, but pointed out that part of the road where it happened had been closed due to maintenance work.
Dutch emergency service provider Eurocross said all passengers on the bus had been Dutch nationals.
Dutch King Willem-Alexander and Queen Maxima said their hearts went out to everyone involved in the bus crash.
"Our thoughts are with the next of kin, everyone one who is worried about the fate of their loved ones and the wounded. We feel connected with you during this great tragedy," they said in a statement.
Dutch tour operator Oad on Friday declined to comment on the cause of the accident.
(Reporting by Dave Graham in Zurich and and Rachel More in Berlin, additional reporting by Charlotte Van Campenhout and Bart Meijer in Amsterdam, editing by David Gregorio, Thomas Seythal and Sharon Singleton)

Emergency responders recover a Dutch travel coach following an accident in Susch, Canton of Grisons, Switzerland, 11 September 2026. Several people died and others were injured in a tour bus crash on the road between Susch and Zernez in the Engadin valley on 10 September, according to a statement released by the Grisons cantonal police. EPA/CLAUDIO THOMA
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