The proposal has been launched by the largest party in parliament, the right-wing populist, anti-immigration Swiss People's Party (SVP), which pushed through the referendum in a country known for its direct democracy.
The proposal means that the possibility of seeking asylum and obtaining residence permits will be limited once the population reaches 9.5 million. Family reunifications will also be made more difficult. There are already 9.1 million inhabitants in Switzerland, which in practice would mean that a population ceiling would have to be introduced quite soon.
There is strong opposition to the initiative from other government parties, who call it a "chaos proposal".
"A lot is at stake," says Minister of Justice Beat Jans to La Tribune de Genève.
Just over a quarter of the population of Switzerland are foreign nationals. With the population at risk of hitting the ten million mark, Switzerland would also be forced to terminate a number of international agreements linked to free movement, including with the EU.
The business community also warns that it may become more difficult to recruit qualified international workers to Swiss companies, especially in the construction sector, healthcare and IT.
Switzerland cannot manage its skills supply on its own, warns Severin Schwan, chairman of pharmaceutical giant Roche.
According to the opinion polls, it's even, but the no side has pulled back a bit towards the end.
The polling stations close at 12 noon and the results are expected to be ready by the afternoon.
