Kane, 24, was substituted 30 minutes into Sunday’s match after injuring his right ankle in a collision with home keeper Asmir Begovic.
He immediately left the field and went straight down the tunnel.
“I hope it is not a big issue,” said Spurs boss Mauricio Pochettino. “We are concerned but need to wait.”
Spurs meet Swansea on Saturday in the FA Cup, with England playing two friendly matches in the following week.
Gareth Southgate’s men travel to the Netherlands on Friday, 23 March before hosting Italy on 27 March, with the squad being named on Thursday.
And Pochettino added: “It’s the same ankle he suffered with before. He landed and twisted his ankle. He’s positive, he’s happy with the victory for the team.”
England forward Dele Alli was also substituted after picking up a groin injury – and the Spurs boss said: “I don’t believe it’s a big issue, we have to manage him.”
Last season, Kane missed 10 games for his club after suffering ligament damage to his right ankle in Spurs’ Premier League win at Sunderland in September.
He also missed two of England’s World Cup qualifiers – a 2-0 win over against Malta in Gareth Southgate’s first game in interim charge and a goalless draw against Slovenia.
Kane, who has scored 35 goals for Spurs this season, then injured the same ankle again on 12 March 2017, in Tottenham’s FA Cup quarter-final victory over Millwall.
On that occasion he missed four weeks of action, including England’s 1-0 friendly defeat against Germany and a 2-0 win over Lithuania in a World Cup qualifier.
‘He looked OK with it’ – MOTD2 analysis
Former Arsenal defender Martin Keown on MOTD2: He’s so important for club and country. Let’s hope it’s not too bad.
“He was out for 49 days the first time he injured that ankle, and 24 the time after that. It looks painful, he is caught by the goalkeeper. He really rocks that but he was up on his feet. We wondered if he may be able to carry on but he hasn’t taken any risks.”
Former Liverpool midfielder Danny Murphy: “What’s important is that he looked OK with it in his body language. He wasn’t carried off on a stretcher. Maybe his previous experience made him cautious and not want to risk it.
“Tottenham only have three games in the next four weeks. Touch wood he’ll be OK.”