"This is a serious epidemic (that) can have neurological effects and complications for pregnant women and birth defects for their baby," Health Minister Marisol Touraine said on France Info radio.
"So I want to very strongly urge women planning to go to Martinique, French Guiana or the overseas territories that, if they are pregnant... They postpone their trip."
Touraine announced mainland France would be sending medical staff to Martinique, a French island in the Caribbean, in the coming days to evaluate the needs of hospitals and doctors.
Zika was first reported in Africa, Asia and the Pacific before leaping to the Americas, where it has been linked to a jump in the number of babies born with microcephaly, or abnormally small heads, particularly in Brazil.
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Zika has spread to some 20 countries in Latin America.
The World Health Organization (WHO) expects it to reach every country in the Americas except Canada and Chile.
A small number of European tourists have been diagnosed with the disease upon their return from Central or South America.