Mourinho did not reveal the nature of the injury to the Ghana international, who joined Real from City's Premier League rivals Chelsea in the close season.
"He has a physical problem and did not recover in time to travel," Mourinho told a news conference at City's Etihad stadium, without elaborating.
After four of six matches, Real are second on seven points in what many consider the toughest group of Europe's elite club competition, one behind German champions Borussia Dortmund.
Ajax Amsterdam are third on four points and City have only a slim chance of making it through to the last 16 with two points in fourth and last place.
Mourinho said he did not think City, who twice squandered the lead in a 3-2 defeat at Real's Bernabeu stadium in September, had any chance of qualifying for the knockout stage.
"Other teams are playing easy groups. Other teams know from day one that they qualify easily," Mourinho said.
"City, Real Madrid and Borussia, we all want to win the competition, we all can but we all know we can be out in the group phase," added the Portuguese, who won the Champions League with Porto in 2004 and Inter Milan in 2010.
"I think City will be out of the Champions League. They can win tomorrow because they have a team to compete against Real Madrid and why not?
"They can do the same against Borussia but eight points is not enough so I think City will be the big team that will be out.
"That win [against City at the Bernabeu] was crucial for us to be at the moment, I am not saying in a completely safe position, but in a position where we depend only on ourselves and we are in good conditions to qualify."
