In a report issued on Monday, Travail.Suisse said it made the finding after studying 46 collective agreements covering 1.5 million employees.
It found that 52 percent of workers under the agreements studied had just a single day for paternity leave, which is the legislated minimum in Switzerland.
Only three percent of male workers were eligible for more than ten days paternity leave.
This compares with a minimum maternity leave of 14 weeks for women.
Travail.Suisse is calling for a minimum of 20 days paternity leave to be paid at 80 percent of normal pay with funding through the system of deductions used to finance maternity and other kinds of leave, such as military service.
Even this proposal would pale in comparison with the paid parental leave provided in Scandinavian countries, such as Sweden, where parents are entitled to 480 days of parental leave when a child is born or adopted.
The Travail.Suisse study found that larger companies and public employers offered the most generous paternity leaves in Switzerland.
Mobility, the car sharing co-op, provides a paternity leave of 20 days to its workers.
Clariant gives 16 days, while employers such as Migros (the cooperative retailer), Raiffeisen (the cooperative bank) and IBM Schweiz allow 15 days.
Other major employers, such as UBS, Credit Suisse, Swiss Re, Swisscom, Swiss Federal Railways (SBB) and Ikea, offer 10 days.
Swiss Post, on the other hand, offers only two days’ paternity leave, according to the report.