The passenger was among five French people who were on the ship.
The four other passengers tested negative but would be re-tested, Rist told France Inter radio, adding that French authorities had traced 22 contact cases.
"What is key, is to act at the start and break the virus transmission chains. This is what we are doing with the prime minister, notably with a decree that came out today that will allow us to strengthen isolation measures for contact cases and to protect the population," she said on Monday.
Prime Minister Sebastien Lecornu will hold a meeting on the hantavirus crisis on Monday.
Asked if France had enough masks and tests to cope with a potential crisis, Rist said: "Yes, France is ready."
Passengers from MV Hondius began flying home aboard military and government planes on Sunday after the vessel anchored in the Canary Islands.
Personnel in full-body protective gear and breathing masks had escorted the travellers from ship to shore in Tenerife in an effort that was continuing Monday.
The World Health Organisation recommended close monitoring of the former passengers, and many countries quarantined them.
with AP
