The England striker has been in barnstorming form since the start of the year, scoring 14 goals in all competitions before hobbling off in last weekend's FA Cup victory over Millwall.
It is a similar injury to one the England striker suffered against Sunderland in September which sidelined him for seven weeks - a period in which Tottenham went six games without a victory in all competitions.
Another such loss of momentum could have dire consequences for Pochettino's hopes of at least improving on last season's third-placed finish in the Premier League.
But Pochettino, who pointed out that Tottenham beat Manchester City 2-0 without Kane in October, is confident their results will not tail off again.
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"We are not worried, we are in good condition." the Argentine, whose second-placed side host his former club Southampton on Sunday, told reporters on Friday.
"We hope it will be different. I think the team now is completely different, that was in September. It was a difficult pre-season after the Euros and we are in a completely different level. The team is now more solid.
"We have improved a lot since that period."
Early indications are that Kane's injury is less severe than the previous one, but Pochettino is cautious about setting return dates, even if he said Kane was talking about being back soon after next week's international break.
"It's good that he's positive but we need to be careful," Pochettino said. "We have full trust in our doctors and physios that they will look after him in the best way.
"We hope that he will be back as soon as possible. Harry wants to play tomorrow!"
Tottenham scored six times after Kane departed against third-tier Millwall with Son Heung-min grabbing a hat-trick and Vincent Janssen netting for the first time in open play since joining the club last year.
"We have to find a solution until Harry is available again," Pochettino said. "We have players who can cope with the pressure and it's a great opportunity for Sonny and Vincent."
Tottenham, who could be 13 points behind leaders Chelsea come kickoff on Sunday, will also be without full back Danny Rose but midfielder Mousa Dembele has recovered from an ankle injury.
Victor Wanyama will be assessed on Saturday after sustaining a neck injury against Millwall and right back Kyle Walker is also a slight doubt after injuring his ankle at home on Monday.
(Refiles to add dropped letter in spelling of Janssen)
(Editing by Ed Osmond)
