The England international picked up the problem while stretching to put the ball in the back of the net in the 74th minute. His effort was subsequently ruled out for offside, and Kane limped off the pitch to be replaced by Erik Lamela.
Spurs boss Jose Mourinho noted in his post-match press conference the extent of the injury is still unclear, per injury analyst Ben Dinnery:
Ben Dinnery @BenDinnery
Mourinho on Ndombele. "He’s always injured. He’s injured, he’s not injured, he plays one match. This is the same since the beginning of the season." And Kane... "It is negative, hamstring is always negative. Is it a tear? Is it a small thing? At this moment I cannot say." #COYS
The striker left St Mary's Stadium on crutches, according to Dan Kilpatrick at the Evening Standard:
The 26-year-old will be a huge loss as he is Tottenham's most consistent goalscorer and the undisputed No. 9 in Jose Mourinho's system.
He has netted 11 goals in 20 top-flight appearances so far this term, and Spurs do not have an adequate like-for-like replacement who can go straight into the first team.
As such, manager Mourinho will have to shuffle his pack in order to accommodate Heung-Min Son or Lucas Moura in the most advanced role.
Spurs have had to deal with Kane's absence through injury in previous seasons, and they have largely coped admirably, with Son particularly stepping up.
However, Kane is among the best strikers in world football, and any side would miss him.
As such, Spurs and Mourinho will be hoping he is fit and firing again soon as they continue their campaign to finish in the top four of the Premier League and return to UEFA Champions League action in February with a last-16 clash against RB Leipzig.