Thomas Rohrbach, spokesman for the Swiss federal office of roadways, said the ban applied to all cars with diesel engines in the Euro 5 emissions category.
It includes all VW models as well as Seat, Skoda and others in the VW group.
The ban affects only cars not yet sold or registered, not ones already in circulation. It does not apply to cars now in production with Euro 6 engines, which are not affected by the emissions scandal.
Mr Rohrbach said the ban could potentially affect 180,000 vehicles that have 1.2, 1.6 and 2.0-litre diesel engines.
Volkswagen has said the 11 million vehicles worldwide that contain software involved in the emissions-rigging scandal include some five million cars made by its core VW brand.
The Volkswagen Group includes 12 brands, and the German company has yet to detail fully what cars where were involved.
A Volkswagen statement said some diesel models and model years – such as the sixth-generation Golf, seventh-generation Passat and first-generation Tiguan – are equipped exclusively with the EA 189 engines in which it says there are “discrepancies”.
It did not detail say where in the world the five million Volkswagens were sold.
Volkswagen brand chief Herbert Diess said “we are working at full speed on a technical solution that we will present to partners, to our customers and to the public as swiftly as possible”.
Meanwhile Volkswagen says it is reorganising its North America business under Winfried Vahland, until now chairman of the board of directors at Skoda.
Michael Horn will remain as president and CEO of Volkswagen Group of America, but its US Canada and Mexico markets will be “combined and significantly strengthened” to form a new “North America region”.
Earlier, incoming Volkswagen CEO Matthias Mueller pledged to do everything to win back the trust of the public in the wake of the emissions scandal.
He said after being appointed to the job that “we stand by our responsibility”, but added that “carefulness is even more important than speed”.
Mr Mueller said the company would introduce “even tougher compliance rules” and promised to make VW “an even stronger company”.