The 27-year-old was replaced by West Ham United’s goalkeeper Alphonse Areola in the second half of Les Bleus’ 2-0 victory over Austria on Thursday.
Earlier reports suggested that the calf issue could rule him out of action for the next three weeks.
However, after further examinations, it has been revealed that the former LOSC Lille man could be out for a month.
He has already been replaced by 37-year-old Stade Rennais goalkeeper Steve Mandanda in the French national team.
Maignan joins a long list of Les Bleus stars missing from Didier Deschamps’ squad through injuries.
The Milan goalie started ahead of first-choice goalkeeper Hugo Lloris as the Tottenham Hotspur captain was out with a thigh injury.
With the World Cup fast approaching, the defending champions are sweating over the fitness of several players, including Kingsley Coman, N’Golo Kante, Presnel Kimpembe, Theo Hernandez, Lucas Hernandez, Lucas Digne, Boubacar Kamara, Jules Kounde and Karim Benzema.
Aston Villa duo Digne and Kamara have already been ruled out of the World Cup after suffering injuries not long after receiving their call-ups.
Paul Pogba is also in a race for fitness and is expected on the pitch ten days before the tournament starts.
Maignan’s setback also comes as a blow to Milan head coach Stefano Pioli who has already lost Theo Hernandez and Sandro Tonali to injuries.
Sky reports that Maignan felt the pain in his left calf and will miss Milan’s league fixture against Empoli, both Champions League games against Chelsea, and the clash with Juventus next month.
The game against Hellas Verona could also come too early for Maignan, but the Frenchman should be available for the clash with newly promoted AC Monza.
The next stop for France in what has already been a disappointing Nations League campaign will see them travel to Copenhagen, where they will face Denmark on Sunday.
It will be their final game before they begin their World Cup title defence against Australia on November 22.
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