Sweden's EU minister Birgitta Ohlsson of the Liberal Party called the result of the Swiss referendum "very sad" and "a great disappointment".
Ohlsson told Radio Sweden: "This means that there are good reasons to review future relations between the EU and Switzerland," adding that she thinks Europe is in a period now where it will need much more freedom of movement in order to handle today's tough, global competition.
"Even if Switzerland is not a member of the EU today, they are also very much affected by the rest of the world and dependent on it in order to main their strong economy," said Ohlsson.
The yes-side won the Swiss referendum to limit immigration by just 0.3 percentage points.
While Switzerland is not actually an EU member, it is a member of the passport union Schengen and has a treaty cementing freedom of movement to and from the EU. Around 80,000 EU migrants enter Switzerland every year. They come primarily from countries with relatively strong economies, like Germany, Italy, France and Portugal.
According to the referendum the Swiss government now has to try to renegotiate that treaty.
But according to Marita Ulvskog, a Swedish Social Democrat member of the European Parliament, it will be hard for Switzerland to carry out the reform. She told Radio Sweden that it is hard to use the referendum method in today's globalized world.
"A referendum which is about Swiss people having the right to determine whether or not they want to be a part of the surrounding world, that is simply unrealistic," said Ulvskog, adding that such a matter cannot be settled through a referendum and that it will have consequences, such as the Swiss being excluded from the EU's single market.
But Johnny Skallin of the xenophobic Sweden Democrat Party said it is a good thing that the issue of immigration is being debated in Europe. He told Radio Sweden: "Apparently, a majority of Swiss people see this problems as so big that something needs to be done about it, and that is despite the fact that Switzerland has a strong economy. They still believe something needs to be done about mass immigration into the country."