Aguero - who has suffered a series of hamstring problems during his four years with City - suffered the injury midway through the first half against Ecuador, pulling up holding his left hamstring as he chased a long ball downfield.
He was reportedly in tears in the Argentina dressing room after the match, and was released from international duty immediately.
Argentina team officials have confirmed that the striker, 27, suffered damage to the back of his left thigh, and he will face further tests back in Manchester over the next few days.