Pienaar suffered the injury during the first half of Spurs' friendly victory over Athletic Bilbao last weekend and subsequently visited a specialist.
The South Africa international had surgery on Tuesday morning and will miss the opening weeks of the new season.
The injury means the 29-year-old will miss out on an appearance against his former club Everton when Spurs start the new Premier League season this weekend.
Pienaar will also sit out games against title contenders Manchester United and City, along with the Europa League play-off with Hearts this month.
Source: Team Talk
Source: Team Talk