The case was detected several days ago in "a woman who is not pregnant," the minister said during a visit to French Guiana, confirming information initially given to provided by a doctor.
The couple lives in the Paris area, the minister's entourage said.
"She showed classic signs of the disease," an official said. "She was not hospitalised and is doing well."
Brazil has been the hardest hit country by the mosquito-borne virus, with 1.5 million cases of active Zika transmission.
The World Health Organization (WHO) has said that up to 46 countries have reported some level of evidence of Zika infection and that 130 countries are home to the Aedis aegypti mosquito which carries the virus, meaning the eventual spread of the disease could be enormous
In nearly all Zika cases, symptoms are mild, resembling those of flu. However, the growing belief that Zika can also trigger microcephaly in babies born to mothers infected while pregnant has spread international alarm.
Microcephaly is a congenital condition that causes abnormally small heads and hampers brain development.
There is currently no cure or vaccine against the Zika virus