Spurs arrived at the ground prepared for the game, but both clubs announced the match had been called off after heavy snow had fallen on the pitch.
Grounds staff were working to clear the snowfall from the field when the announcement was made after consultation between the referee and the two managers.
Tottenham released a statement on social media which read: "We can confirm that today's match against Burnley has been postponed due to adverse weather conditions."
Burnley also posted a statement moments later and said: "Due to concerns with the playing surface and surrounding areas, it's been deemed that the game can't go ahead safely."
"It's bitterly disappointing but I think the team made the right decision," Conte told Sky Sports. "You can see, 10 minutes ago they tried to cut off the snow, and now it's worse than before.
❄️ We can confirm that today's match against Burnley has been postponed due to adverse weather conditions. pic.twitter.com/8azBGHf3Pl— Tottenham Hotspur (@SpursOfficial) November 28, 2021
"We want to play football and have great fun, but I think in this situation it is impossible."
Spurs were looking to bounce back from their shock Europa Conference League defeat at Mura in midweek, with new boss Antonio Conte criticising the players for their performance.
The north London club remain unbeaten in the two league games since Conte replaced Nuno Espirito Santo earlier this month.
Due to the postponement, Spurs stay in seventh place in the league table while Burnley remain in the relegation zone.
"As you can see, the pitch recovers every time they clear it," Burnley manager Sean Dyche said. "The referee explained the safety angle as well so it was important to make a decision early.
"It fell that quick and that heavy. It's still quite strong now. [The pitch] can't get rid of the snow that quick. It's the lines being cleared as well -- we would have to stop and clear them. It's a joint decision with everyone concerned.
"We were ready for the game and I made it clear if it could be played we wanted it on -- as did their manager. I can't see how it could go ahead the way the pitch is at the moment."
The Premier League has not confirmed when the match between the two sides will be rescheduled.
Information from Reuters was included in this report.