Raonic was scheduled to play the Brit in the semifinals, but had to cancel because of a tear in his right thigh from his quarterfinal win over Jo-Wilfried Tsonga.
The world No.4 said he will need five to 10 days to recover, a delay putting his participation in the ATP Finals in jeopardy. The elite eight-man tournament starts in eight days in London.
"I'm on the borderline for that," the fifth-ranked Raonic said. "I still have a possibility that I might be able to play."
Raonic is the fourth-seed in the tournament.