Supporters of the proposed ban say minarets represent the growth of an alien ideology and legal system that have no place in the Swiss democracy.
"Forced marriages and other things like cemeteries separating the pure and impure - we don't have that in Switzerland, and we do not want to introduce it," Ulrich Schlueer, co-president of the Initiative Committee to ban minarets, said.
"Therefore, there's no room for minarets in Switzerland."
Switzerland's Muslims have said that the vote is fuelling anti-Islamic feeling in the country.
"The initiators have achieved something everyone wanted to prevent, and that is to influence and change the relations to Muslims and their social integration in a negative way," Taner Hatipoglu, the president of the Federation of Islamic Organisations in Zurich, said.
"We are frightened, and if the atmosphere continues to be like this and if the anti-Islamic hate increases, then the Muslims indeed will not feel safe anymore"
president of federation of Islamic Organisations in Zurich
"We are frightened, and if the atmosphere continues to be like this and if the anti-Islamic hate increases, then the Muslims indeed will not feel safe anymore. This of course is very unpleasant."
Posters have appeared in many Swiss cities showing a dark, almost menacing figure of a woman, shrouded from head to foot in a black burka. Behind her is the Swiss flag, shaped like a map of the country, with black minarets shooting up out of it like missiles.
The cities of Basel, Lausanne and Fribourg banned the billboards, saying they painted a "racist, disrespectful and dangerous image" of Islam.
The United Nations Human Rights Committee called the posters discriminatory and said Switzerland would violate international law if it bans minarets.
There is also an online game, which has proved very popular, in which players can shoot down minarets as they rise up on the skylines of Switzerland's major cities.
Earlier in November, Muslim prayer rooms across Switzerland opened their doors to the public, in the hope of reassuring voters that they had nothing to fear from minarets.
Business leaders have opposed a minaret ban, saying would be disastrous for the Swiss economy because it could drive away Muslims who bank in Switzerland, buy the country's luxury goods, and frequent its resorts.