Cameroon international Njie, signed from Olympique Lyon in the summer as back-up for Harry Kane, was injured in the recent Europa League match against Monaco.
"You never know because every day it's about how the knee responds but maybe two months or a little bit more (he will be out)," manager Mauricio Pochettino told reporters on Wednesday.
Tottenham moved into the top four of the Premier League with victory over Southampton last weekend, with Kane bagging his ninth league goal of the season.
They face Norwich City at home on Saturday looking to consolidate their place in the Champions League spots.
Pochettino was asked whether Tottenham had a chance to win their first league title since 1961.
"Can we win the title? In football, all is possible," he said. "The last 10 games are very important and it's how you arrive there to attack different objectives or achieve important things. It's important how we arrive in the last 10 games."
(Reporting by Martyn Herman, editing by Pritha Sarkar)
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