Sidibe,29, was carried off towards the end of Stoke's 2-1 defeat at the Britannia Stadium, with Potters boss Pulis revealing the extent of the injury after the match.
"It's a cruel blow for Mama because it appears he has snapped his Achilles," Pulis told stoke's official website.
"The medical staff have told me that it doesn't look good for him, although we will have to wait for confirmation from the scan that he will have on the injury.
"If that is the damage though, he will be lucky to play again this season, and that's a big setback for us.''
It is a second cruel blow in 18 months for Sidibe, who missed the start of last season as he was still recovering from a cruciate ligament injury that kept him out for six months.