In the ski resort of St Moritz, in the southeast canton of Grison, a total of 45 centimetres (nearly 18 inches) of snow was recorded on Monday morning, it said.
The weather agency said the high levels of precipitation were due to a cold front which lowered the snow line to 800 metres (2,600 feet).
Rainfall was also higher than usual, with around 100 litres per square metre measured in the town of Santa Maria, also in Grison, the highest level since records began in 1901, Meteosuisse said.
The snowfall also provoked traffic disturbances in the mountains, with the St Bernard, Flüela and Nufenen passes closed, according to ViaSuisse, which reports on the condition of Swiss roads.
The Gothard, Lukmanier and Oberalp passes are also covered in snow, it added.