The 23-year-old lasted 27 minutes of City's 4-0 win against Blackburn Rovers last Saturday before coming off with a groin problem.
The former Atletico Madrid forward had thought he would be fit for the matches against Venezuela and Chile, but doctors have now told him that it would be a risk for him to feature.
"I am almost ruled out," Aguero said, according to EFE. "The doctors say this is a very tricky injury.
"I am sorry that this is happening in this good moment I am going through at Manchester City, I was hopeful of at least getting to play the Venezuela match, but the doctors have told me they will not take risks."
The Argentine has scored eight goals in seven games for Manchester City since his £35m move from La Liga.