While non-essential businesses will close and movement outside will be restricted in the affected regions, schools will stay open and outdoor exercise allowed up to 10 kilometres from home, he said.
The 'Third Way'
"We are adopting a third way, a way that should allow braking (of the epidemic) without locking (people) up," Castex told reporters.
He said the measures were due to an increased number of Covid-19 cases due to a "third wave" of the virus, with some 1,200 people in intensive care in the Paris region alone.
The other regions affected by the new measures notably also include the Hauts-de-France region of northeast France which covers the city of Lille.
Health Minister Olivier Veran said that there were more people in intensive care in the Paris region than during the second wave in November, with hospital capacity now saturated.
First lockdown
Almost exactly a year ago, President Emmanuel Macron ordered France's first national lockdown which was among the strictest in the world, followed by a second at the end of October.
As in previous lockdowns, a form written out or downloaded on the phone will be needed to justify why a person has left the home in areas under the new restrictions.
Residents in affected regions will not be allowed to leave, except for essential business, said Castex.
But Castex said that "while this is not good news" for people living in those regions, the restrictions were less severe this time.
"These confinement measures will not be a repeat of those we imposed in March and last November," said Castex.
Curfew renewed
Meanwhile, a curfew that has been in place nationwide will also relaxed all over France so it ends at 7:00 pm rather than 6:00 pm to take account of the longer days, Castex said.
The handling of the health crisis has consequences for Macron, just over 12 months from presidential elections.
The government is well aware that as well as registering soaring cases, France has made a sluggish start to its vaccination campaign.
AstraZenca roll-out continues
This week it suspended use of the AstraZeneca/Oxford jab this week in line with many European countries after reports of blood clots.
But following a green light earlier from the European Medicines Agency that the vaccine was "safe and effective" the jabs will now resume, Castex said.
"I will get myself vaccinated with this vaccine to show that we can have complete confidence in it," Castex said.
