It is just the latest bout of bad luck to hit Cooper, who has been hampered by injuries and disciplinary problems since undergoing a full knee reconstruction 11 months ago.
Cooper required the operation to clean up a cartilage problem in the same knee and was expected to be out of action for four to six weeks.
But the procedure has been delayed by a week to 10 days due to a cut, which could lead to infection.
The set-back leaves Cooper in a race against time ahead of the Autumn internationals and he insists he will not risk further problems by rushing back.
"It's all pretty tight now, but you never know. I want to make sure I can come back at full strength," said Cooper.
The Queensland Reds star has started the three past Tests for the Wallabies but was under pressure following an error-strewn performance in the 23-19 victory over Argentina last Saturday.
Cooper was charged down in the second-half, allowing Tomas Leonardi to grab a crucial try. But the mistake occurred just moments after Cooper suffered the latest injury.
"I didn't want to kick it, physically didn't feel I could kick the ball, and I was calling for it to be kicked from halfback," he added. "It was the worst timing possible."
The Wallabies kick-off their Test series against France on November 10, before further encounters with England, Italy and Wales.
But they will be boosted by the return to fitness of James O'Connor, who is set to make his comeback in the final match of the Rugby Championship, against New Zealand on October 10.