The Denmark international limped off towards the end of Sunday's 2-0 FA Cup victory over Oldham, leaving Liverpool to see the game out with only 10 men, and scans conducted on Tuesday confirmed he had suffered a calf problem.
Agger has undergone a scan which has confirmed the injury as a strain but further assessment will be required to determine how long he might be out.
Agger had only recently regained his place in the side following injury to Mamadou Sakho.
Sakho was expected to be out for six weeks after suffering a hamstring injury in the loss to Chelsea on December 29, although reports have suggested his recovery is ahead of schedule.
Left-back Jose Enrique is also currently unavailable, still recovering from a knee operation, while right-back Glen Johnson sat out the Oldham game after jarring his ankle against Hull on New Year's Day.