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.”
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.