Kane scored the winner, his second goal of the season, in a 1-0 victory over Sunderland on Sunday but had to be carried off on a stretcher following a collision with defender Papy Djilobodji
The 23-year-old was later seen leaving White Hart Lane on crutches and wearing a protective boot on his right foot.
"We will assess him tomorrow
It was tough, he twisted the ankle," Pochettino said.
"Now he feels pain and we see tomorrow
It's painful and we need to wait.
"I'm sure there may be a problem with his ligaments but it's difficult to assess today
We need to wait."
Kane would most likely have been rested anyway for the EFL Cup match against Gillingham on Wednesday but Spurs travel to CSKA Moscow in the Champions League next week, between Premier League games against Middlesbrough and Manchester City.
A longer lay-off could also mean the forward misses England's World Cup qualifying fixtures against Malta on October 8 and Slovenia three days later.
Eric Dier and Mousa Dembele limped off in the second half against Sunderland as well but Pochettino said both were suffering from cramp, rather than anything more serious
Kane, Dier and Dembele all faced Monaco in the Champions League on Wednesday - although Dembele only came on for the second half - and the trio were involved at Euro 2016 with England and Belgium respectively
"Dier and Dembele only feel cramps in the hamstring, it's not that big an issue," Pochettino said.
"When you're in different competitions, Champions League is a different competition, we spent a lot of energy on Wednesday, it's different to the Europa League
It's new for us so it's important to learn.
"All of them are internationals, they come after a difficult summer, after playing in the Euros
It's difficult with holidays and pre-season and it's difficult to get fit."
Tottenham's victory over the struggling Black Cats means they climb to third in the Premier League table and maintain their unbeaten start to the season.
They managed 31 attempts on goal and had been the dominant force, even before Adnan Januzaj was sent off for a second yellow card late on.
Pochettino had been critical of his side's energy levels in their defeat to Monaco last week but the Argentinian was satisfied, even if it took a hashed clearance from Djilobodji for Kane to break the deadlock.
"It was a good result," Pochettino said
"For the chances we create it's difficult to understand why only 1-0.
"We created many chances but okay, I'm happy with the performance and attitude and the way we played from the first minute
That's the way we need to play every game, not only some games."
Source : PA
Source: PA