Homosexuality was decriminalized in Switzerland in 1942 and same-sex couples can register partnerships, which about 700 couples do annually.
But partnerships do not provide the same rights as marriage, including the possibility of adopting children and allowing one party to apply for citizenship.
Those who oppose the bill are mainly members of certain Christian congregations and supporters of the right-wing populist Swiss People's Party (SVP).
Same-sex marriage is legal in 29 countries around the world, according to the human rights organization Human Rights Campaign.
Among these are most nations in Western Europe, the United States, Canada, Australia, South Africa and a number of countries in Latin America.