Muslims account for about five per cent of Switzerland's population of 7.5 million people, and form the third-largest religious group after the dominant Roman Catholic and Protestant communities.
Freedom of worship is one of the cornerstones of Switzerland's founding constitution.
Criticisms also came from across the Muslim world, with Pakistani religious groups condemning it as "extreme Islamophobia".
Religious leaders in Indonesia, the world's biggest Muslim-majority country, condemned the vote as a manifestation of religious "hatred" but urged a restrained response.
"This is the hatred of Swiss people against Muslim communities," said Maskuri Abdillah, head of Nahdlatul Ulama which has 40 million members.
"They don't want to see a Muslim presence in their country and this intense dislike has made them intolerant," he told AFP.
Ekmeleddin Ihsanoglu, the secretary general of the Organisation of the Islamic Conference, called the ban an "example of growing anti-Islamic incitement in Europe by the extremist, anti-immigrant, xenophobic, racist, scare-mongering ultra-right politicians who reign over common sense, wisdom and universal values".
The Swiss People's Party (SVP) had forced a referendum on the issue after it collected 100,000 signatures within 18 months from eligible voters.
Some 57 per cent voted to ban the further construction of minarets - towers attached to mosques used to put out the Muslim call to prayer.
The result now paves the way for a constitutional amendment to be made.
The result also flew in the face of opinion polls that had predicted a 'no' vote and surprised government ministers who had opposed the ban alongside the bulk of Switzerland's political and religious establishment.
Other European anti-immigrant parties have sought to capitalise on the result, but it was largely condemned elsewhere in Europe.
Carl Bildt, the Swedish foreign minister whose country holds the European Union presidency, called the vote "an expression of quite a bit of prejudice and maybe even fear" and "a negative signal in every way".
His French counterpart Bernard Kouchner castigated the referendum saysing he was "scandalised" by the vote which he said amounted to "oppressing a religion".
"I hope that the Swiss will go back on this decision rather quickly," he told France's RTL radio. "It is an expression of intolerance, and I detest intolerance."
The Organisation for Security and Cooperation in Europe (OSCE) warned the vote had the potential "to create tensions and generate a climate of intolerance against Muslims".
On Monday Europe's top human-rights watchdog said possible violation of fundamental liberties arising from the Swiss ban on minarets could see the heavily-criticised vote overturned.
Thorbjorn Jagland, the secretary-general of the Council of Europe, said the issue raised concerns of whether "fundamental rights of individuals, protected by international treaties, should be subject to popular votes".
"[The ban] raises concerns as to whether fundamental rights of individuals, protected by international treaties, should be subject to popular votes"
Thorbjorn Jagland, secretary-general, Council of Europe
In a statement Jagland suggested that a case may be made to seek a ruling by the European Court of Human Rights condemning Switzerland for violating freedom of expression, freedom of religion and prohibition of discrimination.
A UN human rights expert also warned that the vote restricted religious freedom and violated Switzerland's international treaty obligations.
Asma Jahangir, the UN special investigator on religious freedom, said the ban marked "clear discrimination" against Switzerland's Muslim community and urged the government to take the necessary measures to fully protect their religious freedom.
"As also stated by the United Nations Human Rights Committee a month ago, such a ban is contrary to Switzerland's obligations under international human rights law," she said in a statement released by the UN.
Eveline Widmer-Schlumpf, the Swiss justice minister, said the ban would come
into force immediately, but noted the possibility that the court could strike down the vote.
"The ban contradicts the European Convention on Human Rights," Zurich daily Blick quoted Widmer-Schlumpf as saying, referring to the 1950 treaty outlining the basic rights of member states.
Commenting on the vote, Daniel Warner, a Swiss-American political scientist at the Graduate Institute in Geneva, said wealthy Arab tourists might think twice now about spending their money in Geneva and other Swiss cities.
He added that Switzerland's efforts to mediate in the Israeli-Palestinian conflict as a neutral country could also suffer.