There are several hundred thousand EU nationals living and working in Switzerland, mainly from Italy, Germany, Portugal and France, while some 450,000 Swiss also live and work in EU countries.
One hundred days before elections to the European parliament, in which immigration will be a central issue, the populist right hailed the Swiss verdict as a template for the rest of the EU.
Geert Wilders, the rightwing Dutch populist, called the Swiss result "fantastic'' and called on the Netherlands to follow suit.
Marine Le Pen, leader of France's National Front, said the same about France. "This Swiss victory will reinforce the will of the French people to stop mass immigration," she said.
In Germany, where Euroscepticism is much weaker, the new anti-single currency party, Alternative for Germany, demanded a referendum on immigration.
And in Austria, Heinz-Christian Strache, leader of the far-right Freedom party, which is currently nudging the top of the opinion polls, called for the same.
If mainstream leaders across Europe are alarmed at the implications of the Swiss vote, analysts said, it is also because they know similar results could be expected in several countries across the EU if single-issue plebiscites were held.
ENTÃO PORTUGAL ESTÁ NA LINHA DA FRENTE.E EM POUCOS ANOS ENCHERAM ISTO DE DIFERENTES E NACIONALIZAM-NOS NA HORA PARA PODEREM TER "TODOS OS DIREITOS" PAGOS PELO INDIGENATO QUE TEM QUE EMIGRAR...ISTO DEPOIS DE TEREM ENTREGUE TUDO O QUE TINHA PRETO E NÃO ERA NOSSO COM AS IMENSAS MANIFESTAÇÕES DE "AFECTOS" QUE DAÍ DECORRERAM...E AGORA DEITADAS PARA DEBAIXO DO TAPETE...
DANOS COLATERAIS DA MAIS VIÇOSA INDÚSTRIA DO PORTUGAL MODERNO: A DO PASSAPORTE...