The Argentina striker, who scored the goal that clinched the Premier League for City on the last day of the 2011-12 season, suffered a serious-looking knee injury during the opening day defeat of Southampton.
The former Atletico Madrid star was stretchered off after an innocuous challenge by Saints defender Nathaniel Clyne, leading to initial reports that he could be out for the season, but in the immediate aftermath the player himself cooled fears by suggesting it was likely to be a short-term absence.
And boss Roberto Mancini confirmed the good news, saying he anticipated Aguero, 24, returning within a month.
"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," Mancini told the official club 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."
City are not short of striking options in Aguero's absence, with Mario Balotelli, Carlos Tevez and Edin Dzeko all seasoned internationals and young Swede John Guidetti available unless he is loaned out again.
Mancini added that England duo Gareth Barry and Micah Richards would be ready to return after the international break.
Midfielder Barry has been out for the past four months, while defender Richards suffered an ankle injury playing for Team GB at the Olympics.