Both the government and parliament said the initiative violates the Swiss constitution as well as the nation's tradition of tolerance
The Swiss news agency ATS says the controversial measure was backed by 57 percent of the electorate, with all but one jurisdiction counted. Voter turnout was about 55 percent.
The Swiss government opposed the measure. Opinion polls ahead of the vote predicted the ban would be rejected by 53 percent of voters.
Both the government and parliament said the initiative violates the Swiss constitution as well as the nation's tradition of tolerance.
Right-wing backers opposed to minarets call the structures symbols of militant Islam.
Switzerland, a country of seven million, is home to more than 300,000 Muslims, mainly from Turkey and the Balkans.
The growth of Islam across western Europe has raised concerns among non-Muslims about Islamic influence on local cultures. Protests against building new mosques have taken place in many countries.
France has banned all religious symbols in public schools, including head coverings for Muslim girls.