Glasgow's stand-in skipper sustained a bicep injury during the PRO12 victory over Connacht which puts him out of the running for the Champions Cup opener against Racing 92 in Paris on November 11.
In today's Evening Times, Glasgow coach Gregor Townsend said: “It is a real shame for Peter and disappointing for us.
“With so many guys away on World Cup duty, he had been an important part of our plans.
“We will have to manage the situation and his absence will present an opportunity for someone else to come in at centre?"