Aguero, 32, playing just his third game since recovering from a knee operation, sustained a muscle problem and was taken off at half-time at West Ham in the Premier League on Saturday.
Asked how long the Argentine - who had knee surgery in June - would be out, City boss Pep Guardiola said: "It depends on the injury. When it is minimum it will be 10-15 days. If it is longer it will be three weeks to a month. I don't know.
"When you are four or five months out (with) knee problems, always you have a risk when you come back.
"We tried to handle it as well as possible, just 50-55 minutes a game, but it was not enough to get fit for the next games. He will be back as soon as possible."