The 31-year-old was working his way back to fitness after sustaining the original injury against Tottenham in August and scored on his comeback for the reserves last Tuesday.
However, only 48 hours later he snapped the tendon again in training and must now focus on getting fit for the start of next season.
Stoke boss Pulis told the club's official website: "It's the same ankle but higher up on the tendon this time. It's wretched luck for the lad, who has had more than his fair share of injury setbacks over the past two years.
"But there is no reason why he can't battle his way back to full fitness. I know he has the determination and dedication to do it, and we will give him all the support that he needs. He would definitely have played some part in the second half of our season and he was very close to being ready for inclusion in the squad so this is a massive blow for him and us."
This is the latest in a series of major injuries for Sidibe, who joined the Potters in June 2005 and is contracted to the club until next summer.
The Mali international missed most of 2009 after damaging knee ligaments while he was stabbed in the arm by Togo fans following an African Nations Cup qualifier in 2007.