The initiative was put forward by trade union Travail.Suisse, which argued that four weeks holiday was insufficient because the pressure of work had increased so much in recent decades, causing rising stress and health problems.
But Swiss television said initial figures showed the proposal had been rejected by a clear 67% of voters in a referendum held yesterday (11 March).
The Swiss have a reputation in Europe for being efficient and hard working, a trait that has helped the country attract international companies and do well in competitiveness rankings.
The Travail.Suisse union said the referendum had taken place at a bad time due to serious economic concerns surrounding the eurozone crisis.
"For many voters, it was understandable that current concerns about their own jobs took precedence over the long-term welfare of people and Swiss business," it said in a statement.
"With their fear-mongering campaign, the opponents of the initiative played with the uncertainty of workers."
The main employers' association, which had lobbied hard against the proposal, welcomed the result.
"The 'no' to the holiday initiative means above all a 'yes' to the maintenance of the competitiveness of Swiss companies and the securing of jobs," it said in a statement.
"Adoption of the initiative would have pushed up already high labour costs in Switzerland and burdened business with additional costs of six billion Swiss francs a year."
It had argued that longer holidays would hurt firms already battling to cope with the impact of the safe-haven franc that has soared since the financial crisis, driven in particular by investors fleeing the eurozone.
Average Swiss holiday entitlement is already around five weeks, as many firms offer more than the statutory minimum.
In 2002, Swiss voters rejected a proposal to cut the working week to 36 hours from 42 hours.
Referendums are central to Switzerland's political system of direct democracy, and have been held on topics ranging from health insurance to smoking bans.
In a separate vote on Sunday, Swiss voters narrowly approved a proposal to limit the building of holiday homes, which are seen by many as a blight in Alpine villages.