Posh, who along with Sunderland and Hull City are battling for a spot in the automatic promotion places, may now consider an emergency loan.
Pym has featured 44 times in all competitions for the side this term and is the club’s only experienced stopper.
A temporary signing could therefore be on the cards given that neither back-up goalkeeper Daniel Gyollai, who was signed in the summer from Wigan and has played only in EFL Trophy ties, nor youngster Will Blackmore have made five Football League appearances.
Commenting on the blow, Peterborough manager Darren Ferguson said: “It is a big blow, the boy has been very consistent over the last two seasons, but we have to get on with it, these things happen in football.
“The boy did ever so well to finish the game against Sunderland, he was struggling and when you see the extent of the injury you can see why. He is going to be out between four and six weeks and I have now got to look at my options and one of those would be an emergency loan.
“That is not because I don’t have any doubts about the other two goalkeepers I have got, but the facts are at this stage of the season, they don’t have the experience of playing enough league games. At any other point in the season, I would have no hesitation, but I will speak to them and we will look at our options.
“It is a blow for the boy and when you have a settled back five or six, the players have a great understanding so if we do bring someone in, it will need to be someone that has played in this league and fits how we want to play and if we can do that then great.”
Peterborough United face Swindon Town on Saturday afternoon and Gyollai could be thrust into action should an emergency loan deal not be struck in time.