Fifty-four percent of voters rejected the plan, launched by a citizens' committee last month.
Several cantons allow foreign nationals to stand for public office at communal level, but none at cantonal level.
The French-speaking canton in Western Switzerland is already a pioneer when it comes to civic rights for foreigners.
Foreign nationals have been allowed to vote in communal elections for over 150 years, and in 2000 they were granted the right to vote at cantonal level.
In a 2007 referendum the public granted foreigners the right to stand for office in communal elections, but not at cantonal level.
Some 45,000 foreigners live in the canton of Neuchâtel, around 25 percent of the population.
This foreign contingent could have swung the vote in its own favour but most elected instead to stay at home, Le Temps reports.
Of the 23,700 foreign Neuchâtel resident eligible to vote, only 3,000 cast their ballots.
In all, 38.1 percent of the canton's electorate turned out to vote.