The young animal had been orphaned and was very underfed, the Swiss news agency SDA reported.
The big cat was captured at the end of September near Lungern in the canton of Obwalden, after it walked into a trap.
It was killed after consultations with Kora, a wildlife monitoring and research organization.
Obwalden wildlife manager Cyrill Kesseli told SDA situations like this one arose very rarely. In Switzerland there was nowhere for wild animals to be kept, he said.
Kesseli said the lynx was from a litter born last spring.
The mother had disappeared and the hungry young lynx kept returning to a residential area where people were giving it food.
The wildlife manager said that sooner or later this would have caused problems.
On September 25th a lynx was found shot dead in Schwellbrunn in the canton of Aargau, despite lynx being a protected species.
Lynx were reintroduced to Switzerland in 1971 after having been hunted to extinction at the end of the 19th century.
There are now two lynx populations in the country.