The Denmark international sustained the injury when he fell heavily in the first half and had to be substituted before half-time.
However, there are contrasting reports on the extent of the injury.
Out of action: Agger faces four weeks on the sidelines with a fractured rib
'Daniel has got a fractured rib, so he's struggling a bit,' manager Kenny Dalglish told liverpoolfc.tv.
However, the version offered by Agger's agent Per Steffensen differs slightly.
'It's the worst possible news. He has broken two ribs, and he must keep still for four weeks,' Steffensen told sporten.tv2.dk.
Conflicting reports: Agger's agent says the defender has broken two ribs
He added on tipsbladet.dk: 'Daniel is way down now and I certainly sympathise with him.
'He will miss the two (international) matches against Cyprus and Portugal and there is a match against Manchester United he also misses. 'It's insanely annoying.'
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