McPake injured his shoulder in the 86th minute of City's 1-0 defeat at Dunfermline on Wednesday night and it has been diagnosed as a dislocation.
Speaking to the CT, Chris Coleman said: "It was a bad one and he has got to have an operation.
"The rupture was halfway down his arm and he was in a lot of pain. He has had nothing but bad luck.
"It was very similar to Scotty Dann's dislocated shoulder but we think it is a bit worse. Scott was out for 55 days but we were lucky with him and we think James will be out for a bit longer than that."