Aguero was hurt in the second minute of City's 1-0 win over Everton in the Premier League on Saturday.
Speaking before City's Champions League match against Roma, Pellegrini says Tuesday that Aguero has undergone a scan and could miss "four, five or six weeks."
However, Pellegrini said that he could not be precise with the timescale of Aguero's absence.
Four weeks out would see Aguero miss seven games, including five in the league, in which City is second behind Chelsea.
Aguero is the Premier League's top scorer with 14 goals, and has scored 19 times in all competitions.