The Tottenham striker rolled over his right ankle as he took an early shot in the FA Cup tie.
Kane was under pressure from Lions defender Jake Cooper as he landed before Cristian Eriksen was brought on in the hit man’s place.
Gareth Southgate is set to name his first Three Lions squad since becoming the full-time England boss on Thursday.
The international side take on Germany in a friendly and Lithuania in a World Cup qualifier at the end of the month.
Jordan Henderson is already expected to miss the Three Lions clashes with a foot injury to hand Southgate a horror start to life as boss.
Goal machine Kane has netted 24 times for Spurs this season, including five goals in his last two games.
Spurs chief Mauricio Pochettino is already sweating over his attacking options after admitting before the game he was not sure whether winger Erik Lamela would play again this season.
The Argentine said: “I don’t want to lie to you and give some information that after you use, and you are right to use, but I can’t say one, two weeks, three weeks, one month or maybe next season, I don’t know,” Pochettino said.
“It’s too difficult my position because we are assessing him every day, how he is in the morning, we prepare a plan, sometimes he is involved from the beginning in the warm-up with the team, sometimes he feels pain, we change the plan.
“Now it is day by day and we see. We hope he can be available again as soon as possible as that is our idea but we can’t give any more information.”