Kane injured his right ankle - the third time he's injured the same ankle in a year - in the 24th minute of Tottenham's 4-1 win at Bournemouth on Sunday.
Harry Kane is reportedly out until May with an ankle injury.
England will face Tunisia, Belgium and Panama in the World Cup group stage in Russian Federation.
A Tottenham source revealed the injury is as serious as the one that kept him out for seven weeks from September 2016.
He will then miss the semi-finals if they win and four league fixtures after the worldwide break, a potential top four decider against Chelsea and further clashes with Stoke, Manchester City and Brighton.
Meanwhile, the report claims that he will miss four Premier League fixtures, Saturday's FA Cup quarter-final clash against Swansea and the semi-final if they beat Carlos Carvalhal's outfit.
He left the ground on crutches and had to postpone a scan due to the amount of swelling.
With the World Cup just three months away, national coach Gareth Southgate will also be eager to find out how long Kane could be sidelined for.
The injury occurred after a collision with Bournemouth goalkeeper Asmir Begovic in the first half at Dean Court.