The defender was forced off in the routine 3-0 win after scoring the opener, his first goal in almost two years, before Jamie Vardy's brace eased the Foxes into the fourth round.
Justin might have been a contender for England's World Cup squad owing to the shortage of left-backs, and he was understood to be on Gareth Southgate's 55-man long list for the Qatar tournament.
The 24-year-old will undergo surgery on Thursday night and Leicester manager Brendan Rodgers fears the worst.
"Sadly he is having an operation tonight, he has ruptured his Achilles," Rodgers said. "It is a huge disappointment for us all, having been out before and coming back and getting back to his level. "He probably would have been close to Gareth's plans. We were all hugely disappointed for him after the game. That's two players we have lost to that injury this season.
"He will have his operation this evening and it will probably put him out for the rest of the season.
"We will see how he recovers and go from there. We wish him a speedy recovery, he is an important player and hopefully he can get back bigger and stronger."
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