The foxes' anchorman Ndidi has had surgery and is expected to return to action in June, Rodgers told a news conference.
The 25-year-old was heavily missed during Nigeria's World Cup playoff, which they lost to Ghana on away goal rule.
"It's a shame for us but he'll get ready for next season," Rodgers said.
"He's been a brilliant player for me in my time here. He picked up a nasty injury that has had to have surgery on and he'll recover now until June."
Ndidi joined Leicester from the Belgian side Genk in January 2017 and has gone to establish himself as one of Premier League's top defensive midfielders. He has played 31 games for the club across all competitions this season.
Leicester, 10th in the Premier League, will travel to sixth-placed Manchester United on Saturday.