The Brazilian hobbled off in the 62nd minute after coming off worse in a 50-50 challenge with Adam and the club expects to be without the 25-year-old for at least four weeks.
A statement on the club's official website read: "Following a MRI scan, the Club can confirm that Paulinho has sustained significant ligament damage to his right ankle after a heavy challenge from Charlie Adam during Sunday's win against Stoke City.
"The Brazil international was forced off as a result of the injury and is expected to be sidelined for at least four weeks."
Paulinho had just returned from suspension after seeing red in the club's 5-0 home defeat to Liverpool - Andre Villas-Boas's final game in charge of Spurs - and will now miss the New Year's Day fixture against Manchester United, the FA Cup tie with Arsenal and at least three more matches, including Manchester City at White Hart Lane.
Adam previously injured Gareth Bale on two separate occasions but took to Twitter to state that it was nothing personal against the north London club.
He said: "Just for the record and to the people tweeting me abuse saying so, I don't and never have had anything against @SpursOfficial.
"...And I would never intend to injure a fellow professional."