The measure would oblige the government to reduce immigration from its current level of 80,000 to a reduced level of 16,000 people per year, and so reduce pressure on the country’s resources.
Opponents to the proposed initiatives however argue it would negatively affect the Swiss economy.
In February the country already voted on the re-introduction of immigration quotas.
The proposal was initially put forward by the national conservative Swiss People’s Party and was aimed at limiting immigration into the country through quotas, as it had been before the bilateral treaties between Switzerland and the EU. At the time, the proposal won the approval of the majority of electorate (50.3 percent).
According to Switzerland's system of direct democracy, the initiatives approved in such votes must be written into law within three years, regardless of how unpalatable they are to policymakers and the business community.
The government now has to implement that referendum result, which heated up the relations with the EU.
This week, David Cameron has also vowed to return net migration in the UK to 1990s levels and to curb perks for migrants coming from the European Union.
The British Prime Minister said that one of his major aims is to lower migration from the EU.
Apart from the immigration vote, there are two more referendums in Switzerland on Sunday.
One of them is “Save Our Swiss Gold”, which will set future of the country’s gold reserves and another one is to decide whether to scrap one of Switzerland's biggest tax perks for expatriates.
Reports however suggest that none of the initiatives is set to win support.
