One woman was pulled out alive after being buried by the landslide in the Alpine valley of Misox in Graubünden.
A rescue operation for the three others is ongoing.
The rockslide hit a group of houses in the municipality of Lostallo.
Rescuers have been searching all day on Saturday with excavators and specially trained search dogs.
William Kloter from the Swiss police, who is heading the rescue operations, told local media that he was hoping to find the three missing persons alive.
Swiss President Viola Amherd said she was shocked by the scale of the damage.
“My thoughts are with those affected. I thank the emergency personnel for their tireless efforts in this difficult situation,” Amherd said on X.
The Matterhorn-Gotthard Railway announced on Saturday evening that it would resume operations between Zermatt and the village of Täsch, where buses would be available for onward transportation.
Zermatt in the southern canton of Valais, near the iconic Matterhorn mountain, had been cut off from the outside world on Friday and Saturday after heavy rains and melting snow caused the Mattervispa River to overflow.
Dramatic videos showed the otherwise small river that flows through Zermatt turning into a muddy torrent, partially submerging streets in the popular ski resort.
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Emergency services in the canton of Valais were on high alert over the levels of the River Rhone, which reached its peak on Saturday.
Authorities evacuated 230 residents on Saturday, with the municipality of Chippis particularly affected, as it is situated on the left bank of the Rhone.
Authorities have warned residents to avoid lower parts of their houses, including cellars, stay away from swelling rivers and refrain from parking on bridges.
People were also advised against filming or photographing the floods for safety reasons.