"It is a stupid injury," Mancini told a news conference. "It was not his fault but he can't play with this injury; for one day, 10 days or two weeks, I don't know."
Mancini, who has Aguero's fellow Argentine Carlos Tevez available again, would not give details of the injury.
"I'm really disappointed. I hope [it's not weeks] because we can lose our top striker for stupid things. He couldn't play against Stoke and can't play tomorrow. I hope he can recover for Arsenal next weekend."
City, who are three points behind Manchester United, can return to the top with victory over Sunderland as United are not in action until Monday away against Blackburn Rovers.
Tevez has made two appearances as a substitute since patching up his relationship with the club following his refusal to warm up in the Champions League against Bayern Munich in September and Mancini said the former talisman could be ready for a larger role in City's eight remaining league games.
"He is improving but I don't think he can start," Mancini said. "But I think he can play more time, he is improving every week."
City could also welcome back defender Vincent Kompany after he missed the last four games with a hamstring injury.
The Belgian used his Twitter feed to relay the good news on Friday, saying: "Just had my second training session with the team. If all goes to plan I will be available for the Sunderland game."
He also called on the City fans to get behind the team after odds on the club's first title since 1968 lengthened because of United's surge to the top of the table.
"It's the last eight games of the season, I hope the fans are ready to be as loud as they have ever been and we'll make sure to be at our best."
