The Belgian limped off after 59 minutes on Wednesday evening and has since undergone a scan to confirm he will need a spell on the sidelines.
“The doctor had to review the scan this morning, and he will be out between four and six weeks,” said the City boss.
“It is a big blow. But we have to move forward. I am not saying that nobody doesn’t know about how important he is.
“Unfortunately for him and for us, he will be out for an important part of the season and we have to find a solution because everyone is struggling in this situation and we have to adapt.”
Walker was also forced to come off against Villa after picking up an impact injury and Pep said: “Kyle had a big impact kick in his hip, but just a kick, so is not available tomorrow but we wish he is available for the next game.
“Nathan is still not ready, but Aymeric came back to training and Eric also came back to training.”
Sergio Aguero has been isolating after it was conformed he had the Coronavirus.
Pep revealed: “What we wish right now is that Sergio feels better.
“He felt uncomfortable in the first three days after testing positive. He felt quite tired, with all the symptoms you get.
“Hopefully, he can come back soon. Step by step in training. A long time we have missed our best striker.”
No further injuries or absences to the squad were reported by the City boss.