Kane is set to spend four to six weeks on the sidelines after damaging ligaments in his right ankle during last weekend's FA Cup win over Millwall.
Spurs manager Mauricio Pochettino said on Friday the 23-year-old was hopeful of returning within a month but it is understood 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 heavily on Vincent Janssen, who has 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."