Rodgers admitted that the right-back's absence would be a blow to his side, but hopes that they can cope without him for the four games that he anticipates he will miss.
"It's a disappointment because I think he's made a good start and he was excellent against Manchester United. Fortunately for us, with the way it works out and the international breaks, he'll probably only miss about four Premier League games," Rodgers told reporters.
"I trust the players and the players we'll put in and we'll be able to cope with that. Glen is the type of player that you never realise how much you miss him until he's not there. He played a lot of games last season and sometimes you can take that for granted with him. Roy [Hodgson] was maybe thinking the same - and then he didn't play for England.
"He'll go away, work hard and keep himself in the best shape he can. We're hoping over the course of the next five weeks he should be back."
Johnson is thought to be eyeing Liverpool's trip to Newcastle United on October 19 as a potential return date.