The snow has blocked all roads and the train leading to the resort in the southern Swiss canton of Valais, which was also hit by some power outages, head of the train station Janine Imesch said.
There are currently 'around 13,000 tourists at Zermatt,' she said, while the station website warned that 'arrivals and departures are not possible at the moment.'
The main access road has been closed since early yesterday, while the train was halted last night, she said.
Zermatt is home to about 5,500 inhabitants and has the capacity to accommodate 13,400 tourists spread across hotels and rental apartments.
But the stranded tourists will not be able to take advantage of the abundant snow for the time being, due to the high risk of avalanches in the area.
'It is not possible to do downhill or cross country, but that's OK. It's a bit romantic,' Imesch said, adding: 'There is no panic.'