Driven by concern about immigration, pressure on public services and housing, the constitutional change pitched by the right-wing Swiss People's Party, or SVP, would mandate that the population must not exceed 10 million by 2050.
Official projections put it on track to do so by the early 2040s.
The unprecedented scheme to dictate population levels by law sits alongside burgeoning efforts by the political right in Europe to set tougher curbs on immigration, fed by discontent about the cost of living, weak economic growth and crime.
"If it goes above 10 million, it will become tight, and immigration should be restricted," said Helen Gulea, a 58-year-old seamstress and part-time kiosk worker in Zurich, originally from Kenya, who voted by post for the cap.
Results of the vote are expected to begin coming in from around midday on Sunday (8pm AEST).
If the proposal were adopted, reaching the 10 million mark would trigger a process that could make Switzerland scrap its free movement of labour agreement with the EU, whose member states supply much of the Alpine country's workforce.
Switzerland's ageing population is already above nine million and polls suggest public opinion is finely balanced.
A final survey this month showed opinion turning against the proposal. An earlier poll had suggested it could pass.
Patrick Leisibach, a migration expert at think-tank Avenir Suisse, said concern was now widespread that overcrowding was stretching public infrastructure to the limit.
"There's a traditional anti-immigration vote on the right wing, but these days even many on the left are feeling the pressure," he said.
Under its system of direct democracy, the Swiss electorate generally votes four times a year on national referendums, which also require the support of the majority of its cantons to pass.
The government and parliament have urged voters to reject the SVP's so-called "sustainability initiative" as folly at a delicate time for Switzerland's export-oriented economy.
In 2025 President Donald Trump slapped the highest US tariffs in Europe on Swiss goods, and the prospect of a population curb could complicate corporate planning.
But SVP lawmaker Thomas Matter argued Swiss gains in prosperity had not kept pace with overall immigration and the country needed to step on the brakes.
Weeks before Trump returned to power, Switzerland sealed a deal with Brussels to deepen economic integration with the EU.
That, and other agreements governing bilateral trade relations, could be cast into doubt by a population cap with free movement a pillar of the EU single market.
