The 29-year-old has yet to feature this campaign after sustaining the injury in pre-season and the club have decided he needs surgery to fix the problem.
France's first match of their World Cup defence is against Australia on November 22 and Allegri has ruled out Pogba appearing for his side this year.
"This morning Pogba trained for the second time, but then stopped, and it was then decided that he undergo surgery," Allegri said on Monday during a press conference ahead of their Champions League opener against Paris Saint-Germain.
"We will realistically get him back in January.
"The World Cup is not my problem, Juventus' problem is that he comes back in January."
Pogba rejoined Juventus this summer after his contract at Manchester United expired - six years on from his move to Old Trafford from the Serie A side for a then world-record £89million transfer fee.