The draft bill, which was narrowly passed by the lower house last September, was opposed by the senate after a debate on Thursday, reported news agencies.
The proposal by hardline Swiss People’s Party (SVP) MP Walter Wobmann called for a federal ban on the burqa, niqab and other full face coverings in public, along the same lines as a cantonal ban that came into effect in the Italian-speaking canton of Ticino in July last year.
In March Wobmann launched a popular initiative to that effect, which has until September 2017 to gather the required 100,000 signatures to take the issue to a referendum.
On Thursday the senate followed the recommendation of a commission on the subject which advised against implementing a ban nationwide, saying it was not necessary since so few people in Switzerland wear the veil.
Such a ban could hurt tourism to the country, it added.
Speaking during the debate, Socialist Anita Fetz agreed with the commission, saying it wasn’t a widespread issue in Switzerland.
“Even among tourists, cases are rare. I’ve seen perhaps two to three tourists entirely veiled in Basel in my whole life,” she said.
Senator Werner Luginbühl agreed, saying while he saw the veil as a form of discrimination against women, there was no need for a constitutional change to solve a problem that does not exist.
"There are probably more people who hike naked than wear the burqa," added Andrea Caroni, a senator from Appenzell Ausserrhoden where naked hiking is in fact banned. In pointing that out he was arguing in favour of the cantons regulating such matters that affect them rather than the federal government.
Ticino senator Flippo Lombardi disagreed with the commission’s stance, saying the Ticino ban had not had any negative consequences, such as a reduction in tourists from the Middle East, as was feared. Therefore imposing a nationwide ban would not be problematic.
The ban is not directly about the burqa, but about covering the face, he added, saying a ban could also be beneficial in combating hooliganism, for example.
The debate concluded that it was not for the federal government to impose such a ban, but that it should be left to individual cantonal authorities to decide if it was necessary in their region.
However the Swiss people are likely to have the final say if the popular initiative goes to a referendum.