The models implicated include Audi, Seat, Skoda, Volkswagen and VW utility makes using an EA 189 diesel engine.
But the total, based on an internal evaluation by Volkswagen, does not include cars sold by independent Swiss garages, said AMAG, which is the exclusive importer of VW products into Switzerland.
The importer said owners of the impacted vehicles will be individually contacted about technical solutions to correct the emissions problem and dates will be set for getting the work done at different dealerships.
Volkswagen pledged that the work would be done at no cost to owners.
It added that cars impacted by the scandal remain mechanically sound and roadworthy.
Amag said it had decided to immediately halt the sales of several hundred new cars requiring emissions modifications.
The Federal Roads Office in Bern announced on Monday night that it intends to to prevent the registration of new vehicles and used cars from abroad that have potentially manipulated emissions systems.
The office said that used cars in Switzerland and those already registered are not affected by this decision.
“Personally, I regret profoundly what has happened,” AMAG CEO Morten Hannesbo said in a statement.
“Manipulation should not happen and I am sure that Volkswagen AG will do everything to resolve this incident and to improve the processes in the future.”
Regardless of how investigations turn out, AMAG is committed to fixing all affected cars free of charge and as soon as possible for the customer once Volkswagen “submits an appropriate solution”.
Meanwhile, German prosecutors on Monday said they were investigating former Volkswagen Group CEO Martin Winterkorn over his connection to the growing emissions scandal.
Winterkorn, who resigned last week, has said he knew nothing about the faulty emissions systems.
VW sparked global outrage when it admitted that 11 million of its diesel cars worldwide are fitted with so-called defeat devices that activate pollution controls during tests but covertly turn them off when the car is on the road.
Former Porsche boss Matthias Mueller was named on Friday to take over from Winterkorn.