The 25-year-old Kane has endured ankle problems in the past, with an issue in 2016 forcing him to miss several weeks.
Spurs face a striker shortage for the remainder of January with Harry Kane having picked up an ankle injury during Sunday's defeat to Manchester United and Son Heung-min having now joined up with South Korea at the Asian Cup.
The striker hobbled off the field after the final whistle at Wembley after a collision with Phil Jones and Victor Lindelof.
'He will continue to be monitored by our medical staff as he commences rehabilitation and is expected to return to training in early March'.
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Another attorney for Rodgers, Lydia Agu, said she received a letter a year ago from Kelly, 51, saying, "Please advise Ms. Rodgers says she met Kelly in San Antonio at a party after one of his concerts.
If Kane does not return until March he will miss the second leg of the Carabao Cup semi-final against Chelsea at Stamford Bridge on January 24 as well as the Premier League clash at the same venue on February 27.
Kane on Tuesday night tweeted: 'Injuries are part of the game but no one will be working harder to get back fit'.
Borussia Dortmund will visit on February 13 for the first leg of a UEFA Champions League Round of 16 match.
Moura missed last weekend's defeat with a knee injury and has been a key attacking outlet for Spurs this season, scoring eight times in his 29 appearances. Four Premier League matches and a fourth-round FA Cup tilt with Crystal Palace are also upcoming.
And Kane's absence will be an arguably bigger hit to Pochettino's side, with the 25-year-old in the midst of another prolific campaign and Heung-min Son now on worldwide duty at the Asian Cup with South Korea.