The 25-year-old Argentina striker has been in stunning form of late, scoring 12 goals in his last 11 games to take the 2012 champions to within three points of league leaders Arsenal.
However, after opening the scoring in Saturday's 6-3 victory over Arsenal at the Etihad Stadium, he had to come off in the 49th minute with a calf problem.
"I think he will be at least one month out," Pellegrini told a press conference, ahead of City's League Cup quarter-final tie at second-tier Leicester City on Tuesday.
"He has a calf injury. Maybe the doctor can say exactly how many weeks he will be." Aguero verified the news on Twitter, but expressed optimism ahead of the rehabilitation process.
"It's confirmed -- my calf injury will leave me out for at least a month," he said. "The good news is recovery work starts today. We started with therapeutic massages on the area and some bike work. I'll keep you posted. Thanks for the support."
Aguero's injury arrives at an inopportune time for City, who face Fulham, title rivals Liverpool and Crystal Palace over the busy festive period.
Aguero also stands to miss league games against Swansea City and Newcastle United, as well as a trip to Blackburn Rovers in the FA Cup third round on January 4.
The former Atletico Madrid player has been key to City's impressive early-season goalscoring form, striking up a partnership with new signing Alvaro Negredo that has seen the two players plunder 32 goals between them in all competitions.
Pellegrini is likely to turn to either Edin Dzeko or Stevan Jovetic to deputise in Aguero's absence, although he could elect to field an extra attacking midfielder and deploy Negredo as a lone striker.
Jovetic recently returned to action following a calf injury, but defenders Micah Richards and Matija Nastasic will miss the trip to Leicester due to respective hamstring and calf problems.
"The players that are injured are Micah Richards -- he continues to be injured -- and Nastasic also, and Aguero," Pellegrini said. "All the other players are available. We will see which 18 players we pick. Jovetic is OK."