The group, called "Yes to a Mask Ban," said it will deliver the petition to federal offices in Bern on Friday, setting up a vote by 2020.
Full-face coverings like niqabs and burqas are a polarising issue across Europe, with some arguing they symbolise discrimination against women and should be outlawed. The clothing has already been banned in France.
"Facial coverings are a symbol of radical Islam that have nothing to do with religious freedom but are rather an expression of the oppression of women," said Anian Liebrand, a Swiss campaign leader. "In Switzerland, we show our faces when we talk to each other."
Others contend bans unnecessarily intrude on religious freedom.
"How many people wear these burqas in Switzerland?" said Oender Guenes, a spokesman for the Federation Of Islamic Organisations in Switzerland, which represents more than 200 mosques.
"You can probably count those living in Switzerland on maybe one or two hands. The rest are usually rich tourists from the Gulf."
Two-thirds of Switzerland's 8.4 million residents identify as Christians. But its Muslim population has risen to 5 per cent, largely due to immigrants from former Yugoslavia.
One Swiss canton, Italian-speaking Ticino, already has a similar ban.
At least two demonstrators who wore veils in defiance after the ban went into effect last July paid fines of 250 Swiss francs, Swiss media have reported.
