The England international scored the equaliser at Craven Cottage before being forced off in the 86th minute in Sunday's 2-1 victory.
Scans have since confirmed he has suffered a hamstring strain and will likely not resume training for six weeks.
A Tottenham statement read: "Following scans and clinical assessment, we can confirm that Dele Alli has suffered a hamstring strain, sustained during Sunday's match.
"Dele will now undergo a period of rehabilitation with our medical staff, with the expectation of returning to training in early March."
Reacting to the injury on Twitter, Alli said: “Gutted. I will do everything in my power to return as quick as possible. Thank you for all the messages.”
The former MK Dons midfielder will miss at least eight fixtures across four competitions over the next six weeks.
He will also miss the first leg of Tottenham’s Champions League last-16 tie against Borussia Dortmund on February 13. There is also an FA Cup fourth round trip to Crystal Palace and up to five Premier League fixtures that Alli could miss.
Given he is only expected to resume training at the start of March, Alli will also face a struggle to be fit for the north London derby against Arsenal on March 2 and the second leg against Dortmund three days later.
The news is a further blow to manager Mauricio Pochettino with England captain Harry Kane also ruled out until March with an ankle injury suffered against Manchester United earlier this month.
The club also allowed Mousa Dembele to leave for Chinese side Guangzhou R&F last week.
Tottenham have yet to make a first-team signing this season and it remains to be seen whether the club will now feel compelled to enter the market to ease their growing injury crisis.