The proposal by lawmaker Walter Wobmann of the populist right-wing Swiss Peoples Party (SVP) won 88 votes, with 87 against, the ATS news agency reported.
Wobmann's bill was nearly identical to a measure approved in a 2013 referendum in the Italian-speaking canton of Ticino banning the full-face Islamic veil.
The Ticino ban came into force on July 1, and calls for fines ranging between 100 Swiss francs (USD 100, 92 euros) to 10,000 Swiss francs.
Today's vote may prove to be a largely symbolic move in the protracted process towards an outright ban on the full-face veil.
Lawmakers will almost certainly defer action on the issue until the country weighs in through a referendum, ATS said.
An initiative has been launched to collect the 100,000 signatures needed to hold a public vote on a burqa ban.
Polls say Swiss voters overwhelmingly support a ban, but a vote could still be two years away.
Today's vote came as countries across Europe confront tough debates over the role of individual religious liberties, amid rising anti-Islam sentiment that has partly been fuelled by immigration.
France was this summer embroiled in a row over bans on the burkini, a full-body Islamic swimsuit, in resorts around the Riviera.
A poll published earlier this month showed Britons are strongly in favour of a burqa ban.
Switzerland's population of eight million includes an estimated 350,000 Muslims.
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