The Argentine striker was injured in a strong but fair challenge by Southampton's Nathaniel Clyne in City's 3-2 season-opening home win on Sunday with fears he may miss up to six months with severe ligament damage.
But Aguero should be fit enough to face Stoke City on September 15 following FIFA's international break the weekend prior.
"I don't think Sergio will be out for long and we are hoping he will be back after the international break which is obviously fantastic news for him and for us," manager Roberto Mancini told City's official website.
"We were very worried a couple of days ago because we feared he could be out for six months or maybe even more which would have been very bad news.
"It looked like a very strange injury at the time and because it was his knee, we were obviously very concerned so this news is a relief for everybody."