The Argentinian is likely to be out for the remainder of the campaign after the minor operation.
Aguero sustained the problem during a training session in March and it was further aggravated by a challenge from Ashley Young in the Manchester derby.
The Club's all-time leading scorer has roared up to the tantalising mark of 199 goals in City's title-winning 2017/18 campaign, with 30 in all competitions this season.
He was in particularly devastating form early in 2018, scoring 15 goals in 13 games while fellow forward Gabriel Jesus was out injured.
After the season the 29-year-old will turn his attentions to World Cup glory in Russia with Argentina.
Everyone at the Club wishes Sergio a speedy recovery.