The defender picked up a knock during City's 2-1 Premier League victory over Tottenham Hotspur on Sunday.
Having had the problem assessed, it has been decided that he will play no part in France's latest fixture.
The French Football Federation confirmed on Monday that Clichy will return to his club to receive treatment on a lower back complaint.
National coach Dider Deschamps will now be without the services of an experienced performer against Italy.
He has, however, opted against drafting in an established replacement and Les Bleus have handed a call-up to uncapped Bordeaux left-back Benoit Tremoulinas.
The 26-year-old has figured in national squads before, but is yet to make his first appearance for his country.