Sergio Aguero set to miss one month
There had been fears the Argentinian had suffered major ligament damage when he fell awkwardly early in the 3-2 season-opening win.
But a scan has found no major damage, and City are now optimistic the 24-year-old will be back in contention for the trip to Stoke on September 15.
"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 the club's 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."
Aguero, who scored 23 Barclays Premier League goals for City last season including the dramatic injury-time winner against QPR to snatch the title away from rivals United on the closing day, was carried off 14 minutes into Sunday's match after falling under a fair challenge from Nathanial Clyne.
Later that night, Aguero sought to ease fears by saying the injury was not as bad as it had appeared, although no further announcement had been made by the club regarding his condition until today.
"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," Mancini added.
There was further good news for City on the injury front today, with both Gareth Barry and Micah Richards also ahead of schedule.
Barry suffered an abdominal injury that ruled him out of Euro 2012, but is now back in training and working to catch up after missing the pre-season, while Richards is making progress after suffering an ankle injury while playing for Team GB at the Olympics.
"Gareth will also be ready after the international break," Mancini said.
"He hasn't played any games for almost four months and he needs to build his fitness up, but he is training again and I don't see him being out for any longer than one month and hopefully, maybe just a couple of weeks.
"Micah's injury is more serious and he could be out a little longer, but having said that, with rest and the right treatment, we are hopeful he could be ready in about one month, which again would be great news."