Johnson had already been forced to pull out of the England squad for their upcoming World Cup qualifying fixtures and Liverpool are not sure when he will be fit to return.
A statement on the club's website on Tuesday read: "After being examined by the club's medical staff at Melwood, Johnson is required to rest his ankle this week.
"A further review will then take place to check stability and decide on further management.
"Therefore, Liverpool have not put a timeframe on Johnson's return to fitness at this stage."
The Reds have begun the season well, winning their first three Premier League fixtures 1-0 to assume early leadership of the table.