If the vote is carried, the tiny landlocked country of half a million people will be the first in the European Union to grant foreign-born residents the right to vote in all the country's elections.
Prime Minister Xavier Bettel has billed the election as a chance to boost the democratic credentials of the wealthy duchy, which is nestled between Belgium, France and Germany.
A Yes vote would be "a yes to more democracy, a yes for the youth, a yes for diversity," he told AFP during campaigning yesterday in the capital, also called Luxembourg.
"No other country in the world, apart from Dubai, has our level of democratic deficit," he added.
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The results are expected Sunday evening.
Bettel's Democratic Party, which is in coalition with the Socialists and Greens, proposes to enfranchise foreigners who have been resident in Luxembourg for over 10 years.
Around 35,000 mostly European migrants meet the criterium.
The referendum has deeply divided Luxembourgers, many of whom fear losing even more influence to foreigners who already play a vital role in the economy.
Former prime minister Jean-Claude Juncker's Christian Social People's party (CSV) called for a No vote, while the business community and civil society groups backed the Yes campaign.
Voters are also being asked whether to lower the voting age to 16 and limit ministerial mandates to 10 consecutive years.