Liverpool won the Carling Cup on penalties over Cardiff on Sunday. The match ended 2-2, as both sides scored in normal time and extra time, but Cardiff had three penalties miss the target as Liverpool won 3-2 in the shootout.
The injury to the 27-year-old Agger made the triumph more costly, as Dalglish said, "He's got a fractured rib, so maybe it will be a few weeks."
Agger, a Denmark international, will miss Saturday's match against Arsenal in the English Premier League.
"Anybody that is injured is a miss. Daniel has been playing fantastically well this year, but we'll miss anybody that is not fit and available," Dalglish said.
"The squad is there to cover eventualities, injuries and suspensions - and we'll need to cover for Daniel if he's going to be out for a few weeks."
Liverpool, which is seventh in the Premiership, follows Saturday's home match against Arsenal with a trip to Sunderland on March 10.