Olivier Veran said there was not enough evidence to confirm a link with the coronavirus sweeping the globe but France was taking the cases “very seriously”.
Britain's state-run National Health Service issued the alert at the weekend about a small number of children presenting an unusual set of symptoms, including abdominal pain and inflammation that required admission to intensive care.
In London, health minister Matt Hancock on Tuesday spoke of “early signs that in rare cases, there is an impact of an auto-immune response in children that causes a significant disease.
“It's a new disease that we think may be caused by coronavirus and the COVID-19 virus.”
But he said that while some of the children who have it tested positive for the virus, others did not.
Cases have also been reported in Italy, Spain and Switzerland, Veran told Franceinfo news radio, adding he had received an alert from Paris concerning “about 15 children of all ages”.
The French minister listed the symptoms as fever, digestive problems and vascular inflammation which can lead to cardiac deficiency.
“To my knowledge, fortunately no child has died from these complications which are fairly rare illnesses that can come with inflammation of the heart,” Veran said.
Some of the cases “in France as in England, but not all, have turned out to carry the coronavirus”, causing “some concern and watchfulness”.
“I am taking this very seriously. We have absolutely no medical explanation at this stage.
“Is it an inflammatory reaction which sets off a pre-existing condition in children who have this virus or is it another infectious disease? There are a lot of questions.
The minister urged international and French experts to gather as much data as possible to establish if a link can be made between the coronavirus and the new symptoms, “which until now had not been seen anywhere”.
France intends to re-open primary schools from May 11 and the minister noted that children had largely escaped COVID-19 infection and that serious cases involved those with underlying conditions.