That means Aguero is highly likely to miss the Manchester derby at the Etihad on December 7, as well as two tricky Premier League away trips to Newcastle and Burnley.
He posted to social media: "It's time for me to work to recover from my injury, and your support always makes it so much the better. Thank you all for the motivation.
"And congratulations, team! Towards the Last 16 of the Champion's, and leading our group."