Mendez-Laing has joined Craig Alcock and Tommy Rowe on the sidelines and manager Darren Ferguson is uncertain how long he will be without his new signing.
Ferguson told BBC Radio Cambridgeshire: "If he has pulled it, he could be out a while.
"The injuries are a blow. Alcock, we'd hoped would be back by now, and Rowe is out for a long time. Mendez-Laing, we don't know."
Mendez-Laing recently signed for Peterborough from Wolverhampton Wanderers for an undisclosed fee.