Spurs, who sacked manager Thomas Frank on Wednesday amid an eight-game run without a league win, said Odobert will have surgery. British media reported that he could miss the rest of the season.
"We can confirm that Wilson Odobert has sustained a ruptured anterior cruciate ligament in his left knee," Tottenham said in a statement.
Spurs, who are only five points above the relegation zone, have faced several injury setbacks this season.
Their long list of absentees include forward Richarlison, three defenders and several midfielders including James Maddison, Rodrigo Bentancur and Lucas Bergvall.
Captain Cristian Romero criticised the club's thin squad in an Instagram post earlier this month.
Spurs, who are languishing in 16th place, next host league leaders Arsenal on February 22.