Christophe Castaner said those who do not respect the new rules, would be fined up to 135 euros ($151).
President Emmanuel Macron announced Monday that movement would be limited for 15 days, starting midday Tuesday.
As of late Monday, France reported 6,633 infections and 148 dead, an increase of 21 deaths and 1,210 new cases from the virus known as COVID-19.
The virus emerged in Wuhan, China last December, and has spread to at least 146 countries and territories. The World Health Organization declared the outbreak a pandemic.
Out of 173,000 confirmed cases, the death toll now exceeds 6,600, while more than 77,500 patients have recovered, according to Worldometer, a website that compiles new case numbers.
The current number of active cases is more than 88,500 -- 93% mild and 7% are in critical condition.