The club gave no timetable for his return.
Tottenham have offered an update on the status of Harry Kane and Dele Alli following their respective injuries against Manchester City in the Champions League quarter-final first leg, with Kane suffering "significant" ligament damage in his left ankle.
But the club indicated he could play again this term as he "will continue to be assessed by our medical staff over the coming week".
We are going to do everything to recover him as soon as possible but there is only five weeks of the season to recover.
He added: 'He was so upset after the game, it was such a hard moment for him of course. e feel so disappointed to accept the situation but now it's much better.More news: Measles Outbreak 2019: NYC announces a Public Health Emergency
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Kane has scored 22 goals in 37 appearances for England, who face the Netherlands in the semi-finals of the Nations League on 6 June.
Spurs said of Alli: "The England midfielder will now be assessed to determine his availability for this weekend's [Premier League] fixture against Huddersfield Town".
The second leg of their Champions League tie against City is on Wednesday at the Etihad Stadium. He damaged ligaments in the same ankle in January, which led to him missing almost two months and seven games.
Kane's absence could have huge ramifications for Spurs' season.
However on Friday Pochettino insisted: 'It's a stat that means nothing, Harry is one of the best players in the world and of course we're going to miss him.
Pochettino undoubtedly possesses other capable goalscorers in his squad but it is clear that not being able to call on Kane during the run-in equates to a huge blow, with Fernando Llorente the Argentine manager's only other option at centre forward.