Zika has been declared a world health emergency due to its link to birth defects in newborn babies.
All 16 known Zika cases in Switzerland involved people who had returned from countries affected by the virus, Patrick Mathys of the Swiss federal public health office (BAG) told news agencies on Tuesday.
Two had returned from Brazil and Columbia, one from Guadeloupe and one from Ecuador.
However since Zika does not produce symptoms in up to 80 percent of cases, the number of infected people could be far higher.
Carried by mosquitoes in Latin America, Zika can cause flu-like symptoms in around 20 percent of cases, including a light fever, rash, headache and muscle pains.
Since October 2015 the virus has exploded in Central and South America, with the World Health Organization saying in January that the region may see up to four million infected.
Though causing only mild symptoms in the infected person, health officials suspect Zika infections in pregnant women may be linked to microcephaly, a condition that causes cranial abnormalities in unborn babies.
The number of babies born with the condition has risen sharply in Brazil since the Zika outbreak, where more than 1,000 cases of microcephaly are thought to be related to Zika infection in the mother.
On Monday Reuters reported that Honduras had identified its first case of probable microcephaly in the unborn child of a five months pregnant woman infected with Zika.
Health officials in Switzerland – which got its first two cases of Zika in January – are advising that pregnant women or those wishing to fall pregnant should not travel to the region.
On their return, women should wait at least three months before they try for a baby, says Safe Travel.
Since Zika can survive in sperm and can therefore be sexually transmitted, couples should use condoms for three months after the man's return from the infected area, or for the duration of the pregnancy if his partner is already pregnant.