“We will never exclude measures that are necessary to protect the public,” Olivier Veran told the Journal du Dimanche.
“That is not to say we have made a decision, but that we are watching the situation hour by hour.”
France has been registering around 15,000 new infections per day, and on Friday confirmed the first case of a new coronavirus variant that recently emerged in Britain.
The new strain, which experts fear is more contagious, prompted more than 50 countries to impose travel restrictions on the UK.
Following a snap 48-hour ban on UK arrivals this week, France has reopened its borders — partly to allow French citizens to return home but also to relieve the massive build-up of freight goods.
On Saturday it took delivery of the first doses of the Pfizer-BioNTech vaccine it will use in its mass inoculation campaign.