Kane limped off in stoppage time after his two goals earned Spurs a point at Goodison Park and boss Jose Mourinho was unable to give much detail on the severity of the issue after the game.
Mourinho said that a diagnosis would take place this weekend, with a scan likely depending on how Kane feels on Saturday morning.
"In our last home game against Crystal Palace (a 1-1 draw on Easter Monday), I don't feel we played as well as we did here, even though we created a lot of chances in that game, too.
"I thought the performance, the defending and the pressing was a lot better.
"We did a lot of work during the week – even though we didn't have a lot of time after the Brighton game (on Monday)."