Kane is set to spend four to six weeks on the sidelines after damaging ligaments in his right ankle during last weekend's win over Millwall.
Spurs manager Mauricio Pochettino said on Friday the 23-year-old was hopeful of returning within a month but Press Association Sport understands the club view that estimate as optimistic.
Either way, Kane appears to have a chance of making the FA Cup semi-final against Chelsea in five weeks' time, as well as a north London derby against Arsenal eight days later.
But Tottenham will have to do without their star striker for Sunday's game at home to Southampton and, in all likelihood, the following league fixtures against Burnley, Swansea, Watford and Bournemouth.
"It's a blow, of course, Harry is for me the best player in the Premier League," Vertonghen said.
"He's a miss for us but we do have a lot of options and we saw that against Millwall and when he was out before in October I think."
Tottenham, however, struggled during that period, when Kane missed seven weeks with a similar injury, as Pochettino's men went six games without a victory and five without a goal from open play.
The pressure weighed particularly heavy on Vincent Janssen, who is yet to find the form that saw him finish the Eredivisie's top scorer last season with 27 goals for AZ Alkmaar.
"I know him very well," Vertonghen said. "I knew him in Holland and I've spoken to two players who played there with him every day and who play in the national team and they are confident of his abilities and so am I.
"He's very determined to make it here. The position as a striker is the hardest one in the Premier League. If you see how hard it is, it's difficult for strikers to fill in that role.
"If you look at some top, top strikers - even they struggle to score goals here."
Another summer signing, Victor Wanyama, has endured no such problems settling in as the Kenyan prepares to face his former club Southampton for the second time this weekend.
Wanyama has been one of Pochettino's most consistent performers this season and key to Tottenham boasting the joint-best defensive record in the division.
"I am a big fan of Victor's. He was an unbelievable signing," Vertonghen said.
"For a centre back like me he is a dream. It makes it a lot easier for us to keep clean sheets.
"He is strong in one-on-one challenges and sometimes you think, 'Ooof, what happened there', but he just stands up and keeps going for 90 minutes."
Even more important to Spurs' rearguard, however, has been the form of Vertonghen and Toby Alderweireld, who have each excelled in Pochettino's back three, along with Eric Dier.
Vertonghen signed a new contract until 2019 in December and the 29-year-old believes he is in the form of his life.
"I am convinced that I am having the best season of my career," Vertonghen said.
"The gaffer has helped me with this and to tell me not to be happy with the level I was at, which was OK, but I must push myself every day to become a better player and that needed some time.
"But I've realised at the right moment and that is why I can say this is the best season of my career and the best team I've played in."