The bill narrowly passes through the lower house of parliament. It still has to be approved by the upper house as well as the government before it becomes law.
Switzerland's lower house of parliament backed a ban on face veils, echoing moves by neighbouring France and other European nations.
Tuesday's vote came as countries across Europe confront tough debates over the role of individual religious liberties amid rising anti-Islamic sentiment that has partly been fueled by immigration. In July, France was 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.
The bill was voted through the lower house, with 88 votes in support of it and 87 votes opposing it, and must pass through the upper house and the government before it can become law.
The plan is being backed by right-wing politician Walter Wobmann who also led a successful campaign to outlaw new minarets in 2009.
The face-veil ban joins a list of measures championed by populist and right-wing movements that have polarised the Alpine nation. Such measures have drawn some criticism from abroad, including most recently a referendum ordering curbs on immigration from the EU.
Wobmann, from the anti-immigration Swiss People's Party, has said the face-veil ban will preserve Swiss culture and curb "radical Islam". He is also pushing for a referendum on the issue.
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.
Even if the ban is endorsed through a referendum, Switzerland's government would still need to draw up a law proposal which would then be subject to a final parliamentary approval.
It may have a tougher time passing the upper house of parliament though, where parties that opposed the ban, including the Social Democrats who have a stronger presence.
About 5 per cent of Swiss residents are Muslim and very few wear the face veil (also known as the niqab) or burqa.