The Belgium international is understood to have picked up the knock in a tough tackle at Selhurst Park.
His loss would represent a huge blow for Mauricio Pochettino in his bid to maintain the pressure on leaders Chelsea, who play earlier on Sunday away to Everton.
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Mauricio Pochettino: Spurs dreaming of more than only finishing above Arsenal
Dembele was banned for first four games of the season for scratching at the eyes of Chelsea striker Diego Costa last May in the drawn game that ended Spurs’ title challenge. He has also had a foot injury this season.
But during the second half of the campaign, the 29-year-old and Victor Wanyama have established themselves as the first-choice pairing in the middle of the park for Pochettino.
Elsewhere, the manager will make a late decision on whether to include fit-again England left-back Danny Rose for Sunday’s game.
Rose hasn’t played since January 31, when he damaged medial knee ligaments in the 0-0 draw at Sunderland.
The derby with Arsenal — always a huge occasion, but in this case a game that could guarantee Spurs finishing above their arch-rivals for the first time since 1995 — could be considered too big a fixture to plunge him straight back into.