The Northern Irishman has claimed that a series of injuries have resulted in the 29-year-old needing time to recuperate.
"Glen has played a lot of the season and has had a number of injuries and he has struggled and it has not allowed him to be 100%," BBC Sport quotes Rodgers as saying. "It is an indefinite timeline he will be out."
Johnson joins teammate Lucas Leiva on the injury list, but the Brazilian midfielder claimed on Twitter yesterday that he will be out for a "few weeks".
The Merseyside outfit currently sit fourth in the Premier League table after 22 games.