In-form striker Kane has scored six goals in his last five appearances for Tottenham, but will miss the game at White Hart Lane.
The England international will be joined on the sidelines by Toby Alderweireld and Danny Rose, both of whom have knee problems.
However, manager Mauricio Pochettino is hopeful that the trio will be available for the Premier League trip to Sunderland on Tuesday.
"Toby, Danny and Harry are out. We don't want to take any risks, but hopefully they'll be available for Tuesday," Pochettino said in quotes published on Tottenham's official Twitter account.
Jan Vertonghen was ruled out for a month and a half by Pochettino last week, but the Argentine thinks he could be back in training in as little as three weeks.
Erik Lamela has been unavailable since sustaining an issue with his hip in the Champions League loss to Bayern Leverkusen in November, and the Tottenham boss said his condition will be evaluated again on Friday.
"Jan is much better, but probably three-four weeks more [out]. Erik will come back training with us tomorrow [Friday] and we'll assess him again," Pochettino said.