The game was due to start at 14:00 GMT but despite attempts to make the pitch playable it was called off at 13:10
Referee Peter Bankes said: “They worked as hard as they could but within 10 minutes the pitch was covered again.”
Burnley manager Sean Dyche added: “It fell that quickly and heavily – it’s still quite strong now.”
Tottenham boss Antonio Conte said: “There is a bit of disappointment because we were ready to play but at the same time I think the Premier League has made the right decision to save the situation for the players and fans.
“In these conditions it is not football. I want to have fun. In this situation it is impossible and there is a serious risk for the players.”
This match has been postponed to play at a later date.