The motion was quashed by 134 votes to 55 after MPs said 18 months shared parental leave – at least six months of which could be taken by the father – would be too expensive, reported news agencies on Thursday.
Supporters of the bill, which mirrors policy in several Scandinavian countries, said the idea would allow women to stay in the workforce if they wish, as well as boosting a father's relationship with his child.
But the Swiss government said it would cost up to 1.7 billion francs to finance.
A better way to help Swiss families would be to boost childcare provision in the country, news agencies reported interior minister Alain Berset as saying.
Switzerland has one of the least generous parental leave policies in Europe. Mothers are entitled to just 14 weeks' paid maternity leave – compared with 39 weeks in the UK – and there is no statutory paternity leave. Most fathers are only allowed to take one or two ‘family days' on the birth of their child, though some companies are more generous.
The issue of paternity leave or shared parental leave has long been on the political agenda in Switzerland, with labour groups and the political left arguing in its favour, so far to no avail.
In April parliament rejected a bill to grant fathers two weeks statutory paternity leave, saying legislation wasn't necessary and companies should decide their own paternity leave policies.
But despite parliament's ongoing rejection, the public may be able to have its say in a national referendum.
In May labour groups and family associations launched the popular initiative ‘For a reasonable paternity leave – in favour of all the family' which proposes a minimum four weeks paid paternity leave for fathers, to be taken at any time during the first year following the child's birth.
They have until November 2017 to gather the necessary 100,000 signatures required to take it to the public vote.
It may be the only way to get some kind of paternity leave reform through. Speaking in May in support of the new initiative, labour group Travail Suisse said parliament had rejected the idea 30 times.
Paternity leave across the EU averages at 12.5 days, though some countries such as Sweden allow far more through shared parental leave policies.