The move is widely interpreted as meant to target women who wear the burqa.
Nearly 67 percent of voters in the northeastern Swiss canton of St. Gallen voted in favour of the new law, according to official results, paving the way for it to follow the example of the southern canton of Ticino, where a similar law was introduced two years ago aimed at Muslim veils.
A text stipulating that "any person who renders themselves unrecognisable by covering their face in a public space, and thus endangers public security or social and religious peace will be fined" was adopted by lawmakers in St. Gallen late last year.
That law passed the regional parliament with support from the populist right and centre parties -- but the issue was put to the people after the Green Party and Young Socialists demanded a referendum.
Switzerland's government last year opposed an initiative aimed at creating a nationwide burqa ban, saying it should be up to the regions to determine if such measures are appropriate.
Voters across Switzerland are however expected to be called to vote on the issue next year after the populist right-wing Swiss People's Party gathered the 100,000 signatures needed to put any subject to a referendum as part of Switzerland's famous direct democratic system.
The group which collected signatures, named "Yes to a Mask Ban", includes some political figures who also headed the 2009 ban on constructing new minarets in country.
Swiss cantons that vote in favour of a ban on the face veil will follow in the footsteps of European neighbours France, Belgium, Austria and Denmark.
Anti-Muslim sentiment in Switzerland is on the increase, the Federal Commission against Racism (FCR) told a conference on the matter last year.
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