Aguero sustained the injury in training last month, but the Premier League champions decided to go ahead with the surgery this week, with little else for them to play for this season.
Citizens manager Pep Guardiola suggested that Aguero may be fit to play again this season, but D'Agostino has expressed a more cautionary tone.
Speaking to Radio 10, the Argentine said: "A player has undergone an arthroscopy with 60 days to go before the World Cup. It is worrisome.
"The recovery process will require at least five weeks. When one had old injuries, the recovery process is not as fast as one would like it to be. It's never going to be less than three or four weeks, or even more.
"I imagine that he will not arrive 100% fit with the limited time that is left before the World Cup. "The anatomy is the anatomy. The injury is what it is. He can try but I don't think he will arrive 100%."
The World Cup begins in Russia on June 14, with Argentina's first match taking place against Iceland two days later.