The Denmark international sustained the injury in Sunday’s 4-0 Premier League defeat at Tottenham.
“Daniel has got a fractured rib, so he’s struggling a bit,” Liverpool manager Kenny Dalglish said.
But Agger’s agent Per Steffensen said: “It’s the worst possible news. He has broken two ribs, and he must keep still for four weeks. 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.”
