"We're very, very sad," Tottenham manager Mauricio Pochettino told BT Sport's Des Kelly. "It's going to be tough and we're going to miss him - maybe for the rest of the season. That worries us and of course, it's a worry for him."
Kane, who left the stadium on crutches, appeared to injure his left ankle in the second half of the Champions League quarterfinal first leg after a collision with Manchester City full-back Fabian Delph.
Lucas Moura replaced Kane - who was helped down the tunnel by two members of Pochettino's staff - in the 58th minute of the eventual 1-0 win.
Kane suffered ligament damage in the same ankle in January and missed more than a month of action as a result.
Delph made contact while fighting for possession on the edge of Pochettino's technical area. The two exchanged words as Kane hopped off the pitch on one leg.
"I think (Delph) was lucky not to get a red card," Pochettino said.
Any long-term absence would affect Tottenham's outlook in the Champions League and Premier League. Spurs face City on two more occasions over the next week and a half.