The franc, which the central bank held down at the height of the eurozone debt crisis, firmed slightly to 1.2226 to the euro from 1.2239 late on Friday before the weekend vote.
The yield, or interest indicated, on traded 10-year Swiss debt bonds firmed slightly to 1.026 percent from 1.012 percent on Friday.
A sharp rise in the yield would have been a sign of perceived sharply increased risk for the Swiss economy in view of the referendum vote.
The vote narrowly backed restricting immigration from European Union countries, undermining other economic agreements with the bloc.
The main stock market index in Zurich rose buy 0.27 percent.
"There is little reason why this news should have a big effect on the markets in the short term, " said René Defossez, stock strategist at Natexis bank in Paris.
The effects of the vote were limited in the short term because the decision did not immediately affect the free movement of goods and capital.
But the impacts could be felt further down the line depending on how the EU responded, he said.
The European Commission was quick to say that it regretted the outcome of the vote, with a majority of 50.3 percent, and said it would study how it affected all of Switzerland's relations with the EU.
Defossez commented: "If there are retaliatory measures, such as a reduction of the movement of goods and capital, automatically that would have negative effects in the longer term on growth and the markets."
The European Union was Switzerland's biggest trading partner, he said.
At Berenberg finance house in London, senior economist Christian Schulz said the vote poses a "grave threat" to the Swiss economic model.
"With its special role as off-shore financial centre under global pressure, it may be about to cut off another of its economic legs, if it loses preferred access to the market of 506 million EU citizens," Schulz said.
"We do not expect Switzerland to collapse economically even in the worst case but the distance in wealth between it and its neighbours to diminish," he said.
"For the EU and its members, the Swiss case could be the test case for the looming negotiations with the UK over similar demands," Schulz said, on wider implications and a proposed vote in Britain on continuing EU membership.
"Britain clearly has a much stronger negotiating position as a large EU member."