Switzerland will also hold votes on May 18th on a multi-billion-dollar deal to buy fighter jets from Sweden, which is on a knife-edge, and measures to ban paedophiles from working with children, which is almost certain to pass.
Much of the national debate ahead of the referenda, which are held every three months in Switzerland as part of the country's direct democratic system, has focused on the pros and cons of introducing a minimum wage.
The unions and leftwing political parties behind the "Decent Salary" initiative insist at least 22 francs ($25) an hour, or 4,000 francs ($4,515) a month, is needed to survive in Switzerland, one of the world's most expensive countries.
If the voters agree, the country would go from having no minimum wage to boasting the world's highest, far above the $7.25 in the United States, 9.43 euros in France, 5.05 euros in Spain and the recently agreed eight euros in Germany, set to take effect next year.
Death-blow to many businesses
But the Swiss are not expected to say yes.
According to the latest poll published last week, a full 64 percent of Swiss voters oppose the initiative, with only 30 percent supporting it.
That marks a 12-point drop in support since April, indicating that opponents, who include the government and basically the entire business community, have gotten their message across.
They have warned a minimum wage, and especially such a high one, would be a death blow to many businesses and would weaken Switzerland's healthy economy.
"This minimum wage would put jobs in danger and would make accessing the labour market even more difficult for youths and those with few qualifications," Bern has warned.
Supporters of the initiative counter that higher basic wages would boost the purchasing power of some 330,000 people.
People working in sales and services and farming, or as hairdressers and flight attendants, for instance, generally earn well below 4,000 francs a month.
The cantons of Neuchâtel and Jura have previously voted in favour of regional minimum wages, but on Sunday the nationwide initiative is likely to go the way of a related text voted on last November.
Two-thirds of Swiss voters rejected that initiative, dubbed 1:12, which would have made it illegal for the top wage-earner in a company to make more in a month than the lowest-paid employee made in a year.
Fighter jet deal up in air
Polls have also long indicated the Swiss will nix a deal worth 3.1 billion francs ($3.5 billion) to buy 22 Gripen fighter jets from Sweden.
But the gulf between the two sides has recently narrowed significantly, with a survey last week showing only 51 percent opposed the purchase while 44 percent were in favour.
Critics argue Switzerland does not need new fighter jets and warn they could end up costing far more than the country has bargained for.
The government and other supporters have meanwhile been campaigning hard to stress the importance of the new planes for Swiss security, and observers say the scale could still tip in their favour.
There is little suspense around the third referendum, which calls for convicted paedophiles to be automatically banned for life from working with children.
A poll last month hinted 74 percent of voters welcomed the initiative.
This despite opposition from the government and most centre-left parties, who deem it is too stringent and superfluous, since Swiss law already makes such bans possible.