The proposal had called for adults to be paid an unconditional monthly income, whether they worked or not.
Supporters said since work was increasingly automated, fewer jobs were available for workers. Switzerland is the first country to hold such a vote.
No figure for the basic income had been set, but those behind the proposal suggested a monthly income of 2,500 Swiss francs (£1,755; $2,555) for adults and SFr625 for each child, reflecting the high cost of living in Switzerland. It is not clear how it would affect people on higher salaries.
There was little support among Swiss politicians for the idea and not a single parliamentary party has come out in favour, but the proposal gathered more than 100,000 signatures and was therefore put to the vote under the Swiss popular initiative system.
Critics of the measure say that disconnecting the link between work done and money earned would be bad for society.
But Che Wagner from the campaign group Basic Income Switzerland, says it wouldn't be money for nothing.
"In Switzerland over 50% of total work that is done is unpaid. It's care work, it's at home, it's in different communities, so that work would be more valued with a basic income."