He suffered the injury during Wednesday’s 3-2 loss at Bournemouth and is expected to be sidelined for at least three months.
His absence is a further blow to Tottenham’s depleted midfield, with Pape Sarr and Yves Bissouma currently on international duty at the Africa Cup of Nations.
Head coach Thomas Frank said the injury was "a bigger one" and left the bench without a single recognised midfielder during Saturday’s FA Cup exit to Aston Villa.
Mr Frank said: "I don’t think we, for whatever reason, had the depth in the bench.
"We basically didn’t have a midfielder to replace Archie (Gray) and Joao (Palhinha), so I had a few solutions in my head, if we had to lose one of them.
"We fortunately didn’t."
Spurs could now look to accelerate their plans to bring in midfield reinforcements, though Bissouma is expected to return this week following Mali’s exit from the Africa Cup of Nations.