Wright's trip to see a specialist in Manchester resulted in a double hernia diagnosis.
The 23-year-old had missed the previous two games after experiencing groin pain and the Dons will be without nine players for their Betfred Cup clash against St Mirren with the suspended Shay Logan joining the absentee list.
Wright's injury is a major blow to the team and player after the attacking midfielder returned from a serious knee injury to play an influential role in the Dons' early-season form.
McInnes said: "Scott Wright goes in for a double hernia operation next week, so he will probably be a total of six weeks from now.
"He had a full season out more or less last year with his cruciate and he came back with that added robustness in his play.
"He has clearly been motivated, as is normally the case when you have been denied the opportunity to play football. When you have that taken away from you, that added appreciation of what you have got normally comes out.
"We have seen that this season. He has developed that responsibility, he has been enjoying playing the role we have asked him to play. Scott has been very good.
"It is a blow but injuries are part and parcel of it and I'm sure he will come back in January looking to pick up where he left off."
The self-isolating Ross McCrorie, Lewis Ferguson and Connor McLennan will also miss Aberdeen's third away game inside a week along with the injured Jonny Hayes, Marley Watkins, Dylan McGeouch and Tomas Cerny.
"It's just like the thing," McInnes said. "We don't play for 16 days and then we have three games in six days when the squad is as stretched as it is
"But, as we showed in the early part of the season when we had challenges, it's finding ways to win. We don't need to be perfect but we have to find ways to win in what will be a tricky cup tie for us.
"We have been trying to get maximum rest into the players and set about the task of trying to get into the next round of the cup, because cup football is all about that anyway.
"You don't need to be perfect on the day but it's all about winning the game, and that's what we aim to do."