Final results showed 50.3% voted in favour. The vote invalidates the Swiss-EU agreement on freedom of movement.
The European Commission said it regretted the outcome of the vote and would examine its implications.
Fiercely independent Switzerland is not a member of the EU, but has adopted large sections of EU policy.
Freedom of movement is a key pillar of the EU single market - a market which accounts for more than half of Swiss exports.
Switzerland's economy is booming at the moment, and unemployment is low, but many Swiss worry about immigration.
Last year 80,000 new immigrants arrived in Switzerland, and foreigners now make up 23% of the population. It is the continent's second highest foreign population after Luxembourg.AND THEY THINK 23% IS MORE THAN ENOUGH - WHICH IS THEIR RIGHT AS A PEOPLE, AND AS A NATION.
AND THEY DIDN'T HAVE TO HOLD ANY EXTRA NON-CONSTITUTIONAL REFERENDA TO ACHIEVE THIS - UNLIKE THE UNDEMOCRATIC EUSSR.
THE ENTIRE WEST HAS WAY TO MUCH IMMIGRATION - NOT JUST INTERNALLY WITHIN THE EU, BUT CHIEFLY BETWEEN THE WEST AND THE EAST.
A CHIEF PROBLEM HAS BEEN MULTICULTURALISM:
IMMIGRANTS WHO HAVE IMMIGRATED SINCE THE ADVENT OF MULTICULTURALISM HAVE NT ASSIMILATED AND THIS HAS LED TO WIDESPREAD ALIENATION AND DIS-INTEGRATION AND A WEAKENING OF THE FOUNDATIONS OF WESTERN CIVILIZATION.
AND THE VACUUM HAVE BEEN GETTING FILLED WITH THE AGGRESSIVE IDEOLOGIES OF WITH UN-DEMOCRATIC SOCIALISTIC STATISM AND ISLAMISM.
AND PEOPLE DON'T LIKE IT.
HENCE THE VOTE.
I HOPE THIS ANTI-EU FEELING GROWS AND THAT NIGEL FARAGE OF UKIP AND GEERT WILDERS OF HOLLAND'S FREEDOM PARTY ASCEND TO LEAD THEIR NATIONS AND DISSOLVE THE EU AS ANYTHING BUT A OPEN MARKET AND FREE TRADE ZONE.