The changes to the animal disease act were supported by 68.3 percent of voters, although less than 28 percent of the electorate participated in the referendum.
Voters in only two cantons — Appenzell Innerrhoden and Uri rejected the legislation.
The government and both houses of parliament overwhelming supported the new laws, which Bern argued are necessary to deal with potential outbreaks of disease that could have a significant economic impact on the country.
In particular the legislation is aimed at giving federal authorities the tools to combat and eradicate communicable animal or “epizootic” diseases.
A group of farmers opposed to mandatory vaccinations were unable to persuade the majority of voters to support their position.
Among other voting results on Sunday, citizens in the canton of Neuchâtel rejected a proposal go tax individuals with assets of more than one million francs over a four-year period.
The initiative was proposed by a left-wing group but the canton’s parliament had recommended against the plan by a 61 to seven margin.
In the canton of Fribourg, citizens threw out a plan by the government to abolish electric heaters by 2025 as part of a plan to use energy more efficiently.
Just 11,000 homes in the canton rely on electric heaters to stay warm in winter but those affected were very active in campaigning against the energy plan, according to media reports.
MPs nationally supported a proposal in September to phase out a quarter of a million electric heaters across the country by 2025.
Among other votes on Sunday, citizens in Zurich voted against plans to introduce common classes for students in kindergarten and first grade.
Opponents warned against exposing children to school pressures at too early an age, while advocates had argued the “common” model would allow for a smoother transition from the kindergarten level to elementary school.