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Midfielder will not be able to play for about four weeks due to rib fractures.
In Sunday's match against London's Tottenham, the Dane fell awkwardly on the pitch and had to leave the field in the first half.
"The news is as bad as it could be," said Agger's agent, Per Steffensen. "He fractured two ribs, so he will have to rest for about a month. Daniel is very disappointed. He will miss international matches against Cyprus and Portugal, as well as the match against Man Utd on October 15."
Agger was a regular starter, and now he will likely be replaced by young Uruguayan Sebastian Coates, who came on as a substitute in the match against Tottenham.