Almost two thirds of voters in the Italian-speaking district backed the ban that still needs to be approved by the federal parliament in Bern before coming into effect.
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Campaigner Giorgio Ghiringhelli, who drew up the proposal, said the result would send a message to "Islamist fundamentalists" he said were in Ticino and across Switzerland.
"Those who want to integrate are welcome irrespective of their religion," he said in a statement on the website ilguastafeste.ch.
"But those who rebuff our values and aim to build a parallel society based on religious laws, and want to place it over our society, are not welcome," he added.
Amnesty International said the vote was a "black day for human rights in Ticino".
There are roughly 400,000 Muslims in Switzerland, about 5% of the population.
In 2009, voters backed a ban on constructing new minarets and Switzerland's biggest party, the Swiss People's Party (SVP), has long made opposition to immigration a key plank of its electoral appeal.
"I would also have voted 'yes' if I had been in Ticino. The burqa is a symbol of female oppression," said Christophe Darbellay of the Christian Democratic People's Party on Swiss television, referring to a head-to-toe covering for Muslim women.
But an earlier attempt to obtain a nationwide ban on burqas in public places was rejected by Swiss parliament in 2012. Cantonal assemblies in Basel, Bern, Schwyz, Solothurn and Fribourg have also rejected similar restrictions.
France was the first country in Europe to pass a law banning full-face veils in public, in 2010, and Belgium later followed suit.
The Ticino vote was launched under Switzerland's traditional direct democracy, which allows proposals to be put to the public if enough signatures are collected.
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