The controversial referendum, which asked voters to approve sweeping new powers for Turkish President Recep Tayyip Erdogan, was narrowly won on Sunday though some votes are still to be counted.
Overall 51.4 percent voted in favour, according to figures from Turkish press agency Anadolu, reported by Swiss media.
Among Turkish voters abroad, 59 percent backed the reform, according to Anadolu.
But not in Switzerland, where only 38 percent voted in favour.
That's in stark contrast to many other Turkish communities abroad. Anadolu's figures show 63 percent of Turkish voters in Germany accepted the reform, 73 percent in Austria and 74 percent in Belgium. Voters in France and the Netherlands also backed the reform.
Turkish-Swiss relations were strained in the run-up to the vote after the Turkish foreign minister was forced to cancel a proposed rally in Zurich when the hotel hosting the event pulled out over security fears.
The Swiss government had previously backed the visit despite a request from the Zurich authorities to cancel it.
Turkey then hit back at Swiss tabloid Blick after it published an article urging Turks in Switzerland to vote against the referendum with the headline ‘Vote no to Erdogan's dictatorship'.
The article caused a sensation in Turkey and was slammed by the Turkish authorities in a statement in which it asked the tabloid “to make amends for the lack of respect shown to our president”.
Swiss prosecutors later opened an investigation into alleged spying on Turks living in Switzerland by an unspecified intelligence service based on "concrete suspicions" of espionage.
Sunday's referendum campaign was criticized by international watchdogs.
"The referendum took place on an unlevel playing field and the two sides of the campaign did not have equal opportunities," said Cezar Florin Preda of the joint mission of the OSCE Office for Democratic Institutions and Human Rights (ODIHR) and the Parliamentary Assembly of the Council of Europe (PACE).
"The campaign rhetoric was tarnished by some officials equating 'No' sympathisers with terrorists," added ODIHR mission head Tana de Zulueta.
On Monday opposition parties in Turkey called for the referendum result to be annulled.