The Argentina striker played just seven minutes of the Premier League encounter at the Etihad Stadium before limping off with the problem, sustained in an awkward fall.
Even without Aguero, who has 19 goals in all competitions so far this season, City were able to edge to a 1-0 victory thanks to Yaya Toure's penalty as they closed the gap on leaders Chelsea to three points.
With the crucial UEFA Champions League meeting in Rome to come on Wednesday, Pellegrini did not think Aguero would be able to feature.
"Sergio has a problem in his knee ligament," he told Sky Sports.
"We will see tomorrow [Sunday] how serious it is but it's not good news.
"I don't think he'll be able to play next week.
"We don't know [how bad it is]. We must wait for the diagnosis of the doctor but the important thing is he won't be there for Roma, a very important game."
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