The 24-year-old has been back in his homeland for treatment and was named in the initial Argentina squad for their forthcoming World Cup qualifiers against Venezuela and Bolivia.
However, after checking the progress of the striker's injury, Argentina have decided to allow him to return to his club.
Aguero said on Twitter: "My knee is better but the squad's physicians would rather have me be safe and stick with the treatments until it's completely healed.
"It's a pity to miss out on the national squad matches but I'll be cheering for Argentina from Manchester, while I finish the recovery."
City boss Roberto Mancini said last week that he expected Aguero to resume training early next week and has him pencilled in for a return to action against Newcastle on 30 March.