The Argentinian remains on the sidelines for this weekend's trip to Arsenal after tearing a hamstring in the New Year's Day win over Stoke at the Etihad Stadium.
There has been speculation the 24-year-old forward could be out for several weeks but the club have not put a firm date on his potential comeback.
Mancini said: "Sergio is not available for Sunday. We don't want to take a risk.
"He continues to have treatment this week. I hope he can play against Fulham next game. If Arsenal was the last game (of the season), okay, but like this it is impossible."
Aguero, top scorer with 30 goals last season, made a slow start to the current campaign after suffering a knee injury in the opening game against Southampton.
But he looked back to his best as he took his tally for the season to 10 with goals in his last two appearances before limping off against the Potters.
Mancini expects the likes of Carlos Tevez, Edin Dzeko and Mario Balotelli to fill the void left by Aguero without having to make specific changes to compensate for his loss.
He said: "Sergio is out for one game but this doesn't change (anything) because we have another three strikers. We can change our system any moment, not because we are missing Sergio or other players."
Aguero has also given an update on his condition, tweeting in Spanish to say he needs another week of recuperation.
He added in English: "I need to start in recovery for one more week. Wish I could be there v. Arsenal. I'll be off-pitch rooting for @MCFC."