The move has initially been introduced at land checkpoints and will be extended to airports on March 29 next year.
The Swiss embassy in Moscow said Schengen visas would be available from December 15.
The new system will simplify life for non-Europeans, including Russians, living in Switzerland who will now be able to travel freely across the Schengen zone without having to apply for a visa.
Switzerland became the 25th member of the Schengen zone and is the third country, after Norway and Iceland, which is not an EU member to join the Schengen zone.
So far, Britain and Ireland have abstained from Schengen membership, which among other things grants access to a common police database. And Romania, Bulgaria and Cyprus have yet to meet border control standards required for membership.
The agreement to set up the Schengen zone was signed in Schengen, Luxembourg in 1985.
