Kane has suffered a minor strain to his left hamstring, the club have announced.
"For tomorrow, we can not take a risk".
However, the Argentine boss admitted he feared for Kane's recovery after the match, replying: "We'll see" when asked if Kane would be fit for Saturday. "Tomorrow, it's impossible", Pochettino was quoted as saying by EspnFc during a pre-match conference.
"Yes, you always want all the players available". It's lucky it's not a big problem but he's not going to play tomorrow. But, like always, we beleive in the collective, in the squad and during the season sometimes these things happen. "There is no sense in taking that risk and making the problem bigger".
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Maybe he'll clear all this up this week when he returns to Green Bay after having surgery and recuperating in Southern California. At this time, Rodgers is still yelling over at Barr. "I probably would have had that same reaction".
"I told the players they are not machines and it's so hard to cope with global duty and to then play every three days".
Kane has been in scintillating form in recent weeks, clocking an impressive total of 13 goals in his last 11 games for the North London side.
Spurs are sitting third in the Premier League table and find themselves level with Man Utd on points ahead of the weekend's clash, though they trail Jose Mourinho's side on goal difference.
Though Tottenham shouldn't lose all hope, last season Spurs did not lose a single game without Kane, managing to win five and draw three.
Kane, who has plundered 17 goals for club and country this season, is doubtful for Saturday's visit to United with a hamstring complaint.