Tanganga suffered the injury in Spurs’ midweek defeat to Aston Villa and is likely to miss the start of pre-season training under their new manager.
The injury caps a frustrating campaign for the 22-year-old defender, who has also been sidelined with shoulder and thigh problems.
He managed 13 appearances in total, including six League starts.
Tanganga has mostly played at right-back but was replaced by Matt Doherty for Tottenham’s 4-2 win at Leicester City on the final day of the season as Spurs secured qualification to the Europa Conference League.
Serge Aurier was left out of the squad, with the club saying he was ill, and the Ivorian is expected to leave Spurs in the summer.
Aurier has a year remaining on his contract and is attracted interest from the continent, including his former club Paris Saint-Germain.