The drop in the mercury followed the first snow of the season in non-mountain areas of the country over the weekend, marking a reversal of Indian summer conditions lingering earlier last week.
Other regions where temperatures fell below minus 20C included Adermatt in the canton of Uri and Ulrichen in the canton of Valais.
Lows of minus 4C were recorded in Geneva, Basel and Zurich and highs on Tuesday were not forecast to reach above four degrees across the country, except for southern Ticino, MeteoSwiss, the national weather office said.
La Chaux-de-Fonds, in the canton of Neuchâtel, where it is expected to remain below zero until the weekend, registered a low of minus 12C.
An anticyclone spreading from the Atlantic Ocean to Central Europe was responsible for the clear skies and cold conditions, MeteoSwiss said.
Snow is forecast for Wednesday and Thursday in regions above 500 metres, bringing badly needed cover for mountain ski resorts with bare slopes.
Just seven ski stations are currently operating, including Zermatt in the canton of Valais and Les Diablerets in the canton of Vaud, which can rely on glacier pistes.
More than 15 others are planning to open this weekend but the majority are not scheduled to start the season until December, weather permitting.