The club announced on Monday that the Brownlow Medallist is expected to miss the next five to six weeks.
Cooney suffered the injury in the first five minutes of the Bulldogs' heavy loss to Sydney on Saturday.
In other injury news, captain Brad Johnson is expected to miss the next two weeks after re-aggravating his Achilles tendon and defender Dale Morris will also miss the next two games after injuring his shoulder.
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The fourth-placed Bulldogs, who have now suffered two successive losses, take on Essendon in their final home and away match this weekend ahead of the finals.
General manager of football James Fantasia said despite the injuries, the club was confident it could still achieve success in 2010.
"To lose a player of Adam's quality this close to the finals is obviously disappointing," he said.
"At this stage the best-case scenario is that Adam will return late in September and while this is unlikely, we have not written off Adam's season yet."
He said skipper Johnson had re-aggravated his Achilles injury but believed he would be available for selection for week two of the finals, as would Morris.
The club is also missing Shaun Higgins (calf, thyroiditis) and Easton Wood (hamstring) but Fantasia said it would provide an opportunity for some young players to step up on the big stage, naming Jordan Roughead and Brodie Moles.
"We believe our list is in a very strong position when you consider the young players coming through," Fantasia said.
"We have been very pleased with Jarrad Grant's development and I think we have unearthed a terrific prospect there for the future.
"You could put Liam Jones in the same boat as well, he has really taken his opportunity this year and continues to impress at the AFL level."
While there is doubt over Higgins, Wood is expected to return through the finals.
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