The Federal Office of Public Health said all were linked to travel in the parts of the world where the virus has reached epidemic proportions, 24 heures reported.
Just two months ago Swiss health officials said there were 16 confirmed cases of Zika in Switzerland – but they warned the actual number could be far higher.
In its latest weekly bulletin, the health office said that in 18 cases the country where infection had occurred was known.
These countries were named as the Dominican Republic (four cases), Colombia, Martinique (three cases each), Brazil, Bolivia (two cases each), Ecuador, Costa Rica, the Virgin Islands and Guadaloupe (one case each).
Switzerland doctors and labs in Switzerland have been under an obligation to declare the virus since March 7th.
In most cases the infection is benign and in 60-80 percent of cases causes no symptoms.
In other patients it can cause symptoms including fever, rashes, headaches and muscular pain.
And in rare cases it can produce severe neurological symptoms.
In pregnant women who become infected the virus can affect the foetus resulting in birth defects, including microcephaly where the head is smaller than normal.
For this reason Zika has been declared a world health emergency.
The virus is spread by Aedes aegypti mosquitoes in Latin America, which are not native to Switzerland.
As there is no vaccine or medicine effective against Zika, the health office advises travellers to affected regions to protect themselves against mosquito bites.
Pregnant women and those trying to conceive are advised not to travel to these regions.