The Denmark captain limped off late in his side's 2-0 victory at Anfield, and scans carried out on Tuesday revealed the issue.
A statement released on Liverpool's official website read: "Agger will now undergo further assessment by the club's medical staff to determine the extent of the problem."
Agger, who moved to Merseyside from Brondby in January 2006, will miss Liverpool's Premier League trip to Stoke City on Sunday.
The 29-year-old's injury leaves Liverpool boss Brendan Rodgers with just two fit senior centre-backs - Kolo Toure and Martin Skrtel - as Mamadou Sakho continues his recovery from a hamstring injury picked up in the 2-1 defeat at Chelsea on December 29.
Liverpool head into Sunday's clash at the Britannia Stadium sitting fourth in the Premier League.
