Cooney sustained the injury in the club's eight-point win over Collingwood on Sunday and scans on Monday confirmed the extent of the damage.
Spirited Dogs upset stunned Magpies
Fellow onballer Matthew Boyd, who missed his third consecutive game against the Magpies, is likely to be available for selection against Port Adelaide at Adelaide Oval after shaking off hamstring soreness.
"He's still training and he's in the group - he just didn’t quite come up again, so we think he will be available this week," Bulldogs medical services manager Andrew McKenzie told the club's website.
"He will train on Wednesday and we will assess him from there."
Captain Ryan Griffen has been given the all clear to play this week after copping a knock against the Pies, while Tom Williams should be fit to play after being a late withdrawal on Sunday.
Meanwhile, young Bulldog Mitch Honeychurch's debut could be delayed by a week after a front-on contact charge from the VFL tribunal.
Honeychurch, pick No. 60 in the 2013 NAB AFL Draft, kicked five goals in a best afield performance against Port Melbourne on Saturday.