The 24-year-old injured his knee in a challenge with Southampton defender Nathaniel Clyne on Sunday, with early reports suggesting that he could be out for up to six months.
However, Mancini quelled fears of a long-term injury, telling the club's offical website: "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.
"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."
Aguero is expected to return for City's clash with Stoke City on September 15.