The ballot in northeastern St. Gallen is to be held as voters across the country also determine whether a moratorium on genetically modified crops should become a full-out ban.
St. Gallen is expected to follow the example of the southern canton of Ticino, where a law was introduced two years ago which appeared to be aimed at burqas and other Muslim veils.
A text stipulating that "any person who renders themselves unrecognisable by covering their face in a public space, and thus endangers public security or social and religious peace will be fined" was adopted by lawmakers in St. Gallen late last year.
That law was opposed by the regional government but narrowly passed the regional parliament with support from the populist right and centre parties.
But the issue is being put to the people after the Green Party and Young Socialists demanded a referendum.
Opponents of the law believe it is populist scaremongering and not that St. Gallen already has a law banning face coverings in potentially dangerous situations such as political rallies and sports events.
The text of the proposed law, first drafted following uproar in the canton over a girl who wore a full-face veil to school, is problematic, according to Fredy Fassler, a socialist in charge of security and justice in St. Gallen.
It does not define when a woman wearing a burqa constitutes a danger, and critics "worry the sanctions will be unpredictable and arbitrary", he told daily newspaper Le Temps.
Switzerland's government last year opposed an initiative aimed at creating a nationwide burqa ban, saying it should be up to the regions to determine if such measures are appropriate.
The government has now launched a counter proposal including changes that would see people who force women to wear a burqa or niqab punished with a prison sentence of up to three years or by fines.
All Swiss voters will eventually cast ballots on the issue after the populist right-wing Swiss People's Party gathered the 100,000 signatures needed to put any subject to a referendum as part of Switzerland's famous direct democratic system.
At the national level, the Swiss will vote Sunday on two schemes linked to agriculture and food security, urging a shift towards more environmentally friendly and Swiss-based food production.
The "Fair Food" and "Food Sovereignty" initiatives appear set to fail and are opposed by the canton of Bern, which warns they could send prices skyrocketing and might violate Switzerland's international trade obligations.
Stefan Legge, an international trade expert at the University of St. Gallen, agreed with the government's opposition to the initiatives.
"The agricultural lobby is trying hard to isolate itself from the rest of the economy and international competition," he told the AFP news agency.
The "Food Sovereignty" initiative, which has the backing of Switzerland's powerful farmers' union, calls for a range of measures, including turning a moratorium on genetically modified organisms (GMO) into a total ban.
That moratorium was introduced after a 2005 referendum and has been extended three times to date. It is due to expire in 2021.
Polls indicate people widely oppose GMO use in the country, but despite early signs of support, the initiative looks doomed to fail, according to a survey published this month by the Tamedia group.
Observers put the initiative's shrinking popularity down to another element baked into the text: the call for imports to be limited to food produced under the same social and environmental norms as those applicable in Switzerland.
"No serious analyst can say it is the GMO ban that is sinking the initiative," Michelle Zufferey of the Uniterre union told AFP.
She pointed out that the GMO aspect had barely been mentioned.
"It is the fake arguments about massive price hikes and a lack of choice and about efforts to isolate Switzerland that have hurt our initiative," she insisted.
Swiss President Alain Berset himself warned in a recent interview with Le Temps that if the initiatives were to become law, it would "lead to a price hike".
"For now, unfortunately, everyone cannot afford organic," he said.
He also warned that "imposing Swiss standards on imported food goods would violate agreements reached with our trading partners as well as World Trade Organization rules."