The Brazil midfielder, who had been impressing in his first start under new Spurs manager Tim Sherwood, was forced off 62 minutes into Sunday's 3-0 win after being clattered by the Stoke man.
Adam avoided a booking for the challenge but not the anger of Tottenham fans and staff, as this was the fourth time he has been involved in a high-profile incident against Spurs.
During his time with Blackpool, Liverpool and Stoke, the 28-year-old has previously clashed with Gareth Bale on two occasions and once with Scott Parker.
Tottenham's anger at yet another incident was clear in a statement on Paulinho's condition released this morning, unusually highlighting the perpetrator's role in the incident.
"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," read a statement on the club's official website, www.tottenhamhotspur.com.
"The Brazil international was forced off as a result of the injury and is expected to be sidelined for at least four weeks."
Tottenham are reportedly considering making a formal complaint about the Scotland international, who came close to moving to White Hart Lane from Blackpool in January 2011.
Adam has since become a hate figure with Spurs fans and was booed onto the pitch on Sunday, but rejected the notion of having an issue with Tottenham.
"Just for the record and to the people tweeting me abuse saying so, I don't and never have had anything against @SpursOfficial," he tweeted via his account, @Charlie26Adam. "And I would never intend to injure a fellow professional."
Adam first caught Bale during his time at Blackpool in a Premier League game in May 2011. The Welshman was ruled out for three months with ankle ligament damage.
They clashed again during a pre-season friendly between Liverpool and Spurs in the United States in 2012, after which Bale described Adam as a "coward".
Adam was also sent off after collecting a second yellow card for a foul on Parker during Spurs' 4-0 win over Liverpool in September 2011.