The canton of Ticino thus looks set to become the first region in Switzerland to introduce such a ban.
Following the green light from the regional parliament yesterday, the bill, which was backed by 65 percent of the electorate in a 2013 referendum, could take effect in April, a parliamentary spokeswoman told AFP.
The regional government still needs to give its approval before it can be signed into law, she said.
The bill was inspired by a controversial French law introduced in 2011 barring women from wearing a niqab, a head-to-toe body covering, in the street, public gardens, shops and government buildings.
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Once the law comes into effect, anyone wearing a full-faced veil in the region risks fines of between 100 and 10,000 Swiss francs (USD 98-9,830, 92-9,230 euros).
The bill makes no exceptions for tourists, and Ticino is planning to display warning signs at airports and border crossings to inform visitors of the ban.
Some 40,000 tourists from the Middle East visited Ticino last year.