Zika, which is rapidly spreading through the Americas and has been declared a global health emergency by the World Health Organisation (WHO), is primarily transmitted through mosquito bites.
However, Brazil in the last week announced two cases of transmission through blood transfusions from infected donors.
“Someone who comes from a zone where there is Zika can not give blood for 28 days,” Touraine said in an interview with Europe 1 radio, news channel iTele and Le Monday daily.
She also advised pregnant women to inform the authorities if they had traveled to any of the zones.
Zika has been reported in more than 30 countries since it first appeared in the Americas last year, where it has been linked to thousands of babies being born with microcephaly. This is a condition where infants have abnormally small heads and often have underdeveloped brains.
There is no vaccine or treatment for the virus.
Eighteen cases have been reported in travelers in France, Touraine said.
The mainland part of the country has been spared by the virus, but it has hit some of its overseas territories such as the Caribbean islands of Martinique and Guadeloupe, and French Guyana which neighbors Brazil.