Pogba had the operation in Italy but is expected to recover in time for the start of pre-season training at the end of June.
The 22-year-old suffered a torn thigh muscle against Preston on April 1. The injury came less than a week before Crewe's Johnstone's Paint Trophy win and ruled him out of that game at Wembley as well as the remainder of the campaign.
By that point Pogba had scored 16 goals in 41 appearances for the Alex.
Manager Steve Davis told the club's official website: "Mathias suffered a grade two tear in his thigh and he and his agents wanted him to have surgery in Italy with a specialist. We were fine with that and he has had that now.
"He has been over to be checked out by (physio) Rob (Sharp) and he is fine with it. He will return to Italy shortly to undergo more rehab with the surgeon who conducted the operation.
"It is common practice for foreign players, especially in Italy and France, to have surgery for this type of injury. In Britain, we are perhaps more cautious but we were fine with it and Rob has been kept informed.
"Mathias is on a crutch at the moment but we are sure he will be fine and will return for pre-season training on schedule."