Snow covering train tracks and roads leading in and out of the ski resort are covered, and helicopters have not even been able to take off, according to the Mirror.
A spokesman for Zermatt Tourism said rail staff were unable to remove enough snow from the train tracks to make them operable.
British tourist Belinda Hadden and her friends missed their flight back to London today.
She said there are "worse places to be trapped", but told the paper: "I had no idea until I went to the train station and was told there was no way I was getting out.
"There hasn't been snow like this since 1999, there's been a metre alone today."
Zermatt Tourism said the situation would be assessed at 8.30am tomorrow morning.
Zermatt is a beautiful mountain village with no cars and cobbled streets, and sits in a deep valley dominated by the graceful curves of the majestic Matterhorn.
As Belinda said, we can think of worse places to be stuck for the night...
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