Speaking to French media, Agnes Buzyn said one case of the virus had been confirmed in Bordeaux while the second had been found near Paris - marking the first confirmed cases of the novel virus in Europe.
Shortly afterwards a third case, believed to be a family member of one of those to have already been announced, was confirmed in the country.
The minister, who said both of the initial cases had travelled to China, added that she expects more to emerge within the nation's borders.
"We see how difficult it is in today's world to close the frontiers. In reality, it's not possible," she said
The minister added that she believed the development of a rapid diagnostic test within France was one of the reasons the country had been the first in Europe to confirm a case.
"You have to treat an epidemic as you would a fire, that's to say find the source very quickly," she added.
She confirmed the Bordeaux patient is a 48-year-old Frenchman of Chinese origin, and was taken to hospital after presenting classic flu-like symptoms having passed through Wuhan
They were in contact with about 10 people before he was taken into care, the minister said. French authorities are seeking to contact them.
The second, who also travelled to China, is receiving treatment in a hospital in Paris - although little is known of the circumstances surrounding their infection.
So far 939 cases have been confirmed globally, with 916 of those in China. Some 26 deaths have also been confirmed as having been caused by the disease.
Earlier on Friday a case of the virus was confirmed in Chicago, Illinois - marking the second instance of the illness in the US to be confirmed by the country's Centres for Disease Control.
The agency said it has 63 patients under investigation from 22 states, with two confirmed positive cases and 11 negative, so far.
It comes after a woman who travelled to France from Wuhan was tracked down after claiming she took drugs to mask potential symptoms of a deadly virus at the airport, according to authorities.
Ms Yan posted on Chinese social media that she “took antipyretics and managed to pass through checks at the airport and enter French territory” after suffering from a fever and a cough.
“The Chinese ambassador received calls and emails from several Chinese citizens” about the post, and contacted the woman to tell her to phone emergency services immediately, according to a spokesperson from Beijing's embassy in Paris.