Alli scored a second-half equaliser in the 2-1 win at Fulham but then went off injured in the closing stages.
"Dele will now undergo a period of rehabilitation with our medical staff with the expectation of returning to training in early March," Tottenham said in a statement on their website (www.tottenhamhotspur.com).
The 22-year-old said on Twitter that he was 'gutted' with the news.
"I will do everything in my power to return as quick as possible. Thank you for all the messages," he said.
Alli's absence is another setback for a team chasing a top-four finish and Champions League slot and whose injury problems are stacking up.
Tottenham are third in the league but have talismanic striker Harry Kane out with an ankle injury and South Korean Son Heung-min at the Asian Cup in the United Arab Emirates.
The pair have scored 22 league goals between them this season.
France midfielder Moussa Sissoko has also been out with a groin injury and is unlikely to return in time for Thursday's League Cup semi-final second leg at Chelsea. Spurs won the first leg at Wembley 1-0.
Spurs also sold midfielder Mousa Dembele to Chinese Super League side Guangzhou R&F last week.
Tottenham play Germany's Borussia Dortmund in the last 16 of the Champions League with the timeframe for Alli's recovery making him doubtful for both legs on Feb. 13 and March 5.
"Some injuries appear in a period with a more busy schedule and another opportunity opens the door for players not consistently in the starting 11 or on the bench," manager Mauricio Pochettino said after Sunday's game.
"It is a great opportunity for different players to show quality."
Pochettino fielded Fernando Llorente as a replacement for Kane on Sunday but the experienced Spaniard had a tough afternoon with an own-goal and wasted chances.
Speedy Brazilian forward Lucas Moura is back in training, however, after returning from injury.
(Reporting by Alan Baldwin; Editing by Hugh Lawson and Toby Davis)
