The European Commission said it would assess close European Union ties with non-member Switzerland following the narrow vote, raising the prospect of restricted trade or other retaliatory measures.
Nigel Farage, the head of the UK Independence Party, Britain's main eurosceptic party, said Switzerland had stood up to "bullying" from unelected bureaucrats in Brussels.
"This is wonderful news for national sovereignty and freedom lovers throughout Europe," said Farage, who is a member of the European parliament (MEP).
France's extreme right National Front party praised "the Swiss people's lucidity" in a statement, calling for France to likewise stop "mass immigration".
Austria's far-right FPO party said that country would vote the same way given the chance, while Italy's populist Northern League demanded a similar referendum there.
EU foreign ministers were scheduled to meet on Monday in Brussels but it was not clear whether the Swiss vote would be added to the agenda.
Wolfgang Schaeuble, finance minister of Germany, Switzerland's top trade partner, said the result "is going to create plenty of problems for Switzerland in a host of areas".
But he said it was also a warning sign of European globalization fears.
The Swedish government said it was very unhappy with that Switzerland narrowly agreed to limit immigration from EU countries, according to a report from the TT news agency.
“I am deeply disappointed by the sad outcome of the referendum in Switzerland," said Sweden's EU Minister Birgitta Ohlsson.
"Limiting immigration is going to frame the strong Swiss economy is so dependent on the outside world," she said.
“Europe needs more freedom of movement to get by us in the global competition,” Ohlsson said.
“Now that the country will close the borders for EU citizens , there is reason to look at how relations between the EU and Switzerland will be in the future,” she warned.
Swiss President and Foreign Affairs Minister Didier Burkhalter said he planned to tour European capitals to explain the vote and seek a solution, starting with Berlin.
"The people are sovereign, and a healthy system doesn't force the public to follow political authorities with outsized powers," Burkhalter said.
The German newspaper Tagesspiegel said: "With the (Swiss) referendum, it becomes more likely that the anti-Europeans will represent the biggest group in the European parliament, with a quarter of the MEPs."
In France, the business daily Les Echos, described the result as one with "economic consequences that are difficult to predict".
The vote obliges the Bern government to renegotiate within three years a 2007 deal struck with Brussels that gave most EU citizens free access to the Swiss labour market.
It was one of a series of accords reached in 1999 after five years of talks that were seen as a way for Switzerland and the EU to enjoy access to each other's markets without Switzerland having to opt for full EU membership.
Brussels, though, has warned that Switzerland cannot cherry-pick from the binding package of deals, which were themselves approved in a 2000 referendum.
Besides free movement of labour, the pacts include equal access for Swiss and EU firms to public procurement tenders, smooth trade in farm goods, air transport and other sectors.
'Consequences for all of Europe'
The Belgian newspaper Le Soir noted that "it's the whole scaffolding of Switzerland's bilateral accords with the European Union which is assured of collapse".
Centre-left El Pais, Spain's top selling newspaper, worried about ripple effects of the vote in an editorial called "Perverse Consequences" published in Monday's edition.
"While by a narrow majority (50.3% of votes cast), the victory of those who oppose 'mass immigration' in Switzerland will have consequences for all of Europe," it said.
"Not only does it call into question the agreement on the free movement of people established with the European Union, it also reflects the populist and xenophobic agitation sweeping the Old Continent less than three months before the European elections," it said.
"This is the worst possible outcome for the majority of politicians and Swiss business organizations," it added.
Spanish conservative daily ABC wrote on its website that the outcome of the referendum "caused a real political earthquake in this central European nation and it puts its ties with the European Union in danger".
While concerns have been raised about the impact on the Swiss economy of the vote, the Swiss franc remained strong in currency exchange trading early Monday morning.
The franc was valued at 0.81740 euros, down slightly from 0.82 euros a week earlier.