Though the club would not confirm Kane's likely length of absence, ankle ligament damage typically requires at least six weeks for recovery, with widespread reports claiming that the England striker will be out of action for a couple of months.
Should concerns be realised and the injury fall into the category of grade two ligament damage, Tottenham could well find themselves without their principal forward for a period of between six and eight weeks.
Now, only five games into the season, numerous reports suggest the England worldwide is set for up to two months on the sidelines.
That could mean that 23-year-old Kane, who scored his first Premier League goal of the new season in that win over Sunderland, is sidelined until late November.
Today on Twitter, Kane wrote: "Injuries are never nice but part of the game - working hard to get fit as soon as possible! Will be cheering on the lads while I recover". Spurs are now third in the Premier League table, right where they finished last season, but they have some tough sledding right ahead.
Janssen has been compared with Ruud van Nistelrooy and Klaas-Jan Huntelaar in his homeland, but Pochettino is refusing to get carried away by the hype, adding: "I need to be calm and patient with him".
Tottenham team manager Mauricio Pochettino sought patience when Kane left White Hart Lane on crutches and wearing a protective boot on his right foot.
Kane was in "a good mood" when the pair had been chatting in restaurant together, said Pochettino.
Spurs boss Mauricio Pochettino did not comment on Monday, but he did say this after the match on Sunday: "Kane to be assessed tomorrow".
"Potentially he can be a top player, but now it's how he builds his future that is very important - and it's our responsibility to tell him".
Pochettino said the time off the pitch could be used constructively. He is a striker who can give us a lot of things.
Janssen has received the backing of Tottenham captain Hugo Lloris to successfully deputise for Kane, as the Frenchman said: "We used to say that we have a competitive team and I think we are very confident in every player".