His Spurs team-mate, midfielder Harry Winks, also limped out with an ankle problem, bringing the absentees from the club to three as Dele Alli had already pulled out.
Both Kane and Winks, who has caught the eye for Spurs this season and won his first senior cap last month, suffered the injuries in their club’s win over Crystal Palace on Sunday.
Tottenham boss Mauricio Pochettino said Winks, who went off at half-time in the Palace match, had twisted his ankle.
Kane received treatment on his knee in the first half and was substituted on 77 minutes for “protection”, according to Pochettino.
England coach Gareth Southgate has called up Jake Livermore even though the midfielder’s club West Brom are on a dreadful run of form, having not won in 10 matches.
“Squad update: we’ll be without @HKane and @HarryWinks for this month’s games, while @29_JL has been called up,” read a post on the England team’s official Twitter page.
Southgate, who guided England to the 2018 World Cup finals in his first challenge since replacing Sam Allardyce last year, also has injury concerns over Chelsea defender Gary Cahill and Liverpool midfielder Jordan Henderson.
The latter missed Liverpool’s 4-1 win over West Ham on Saturday with a thigh injury.
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