"Unfortunately I have bad news. The injury rules me out for several months. See you next season," Clerc said on his Twitter feed.
The 31-year-old Clerc, who has scored 38 tries for France, picked up the injury in Toulouse's 39-17 defeat at Clermont in the French Top 14 on Saturday.
France will play New Zealand three times between June 8 and 22.
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