The game at Turf Moor was due to start at 14:00 GMT on Sunday 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."
Spurs suffered an embarrassing loss to NK Mura in the Europa Conference League on Thursday. They will now have to wait until Thursday's meeting with Brentford to regain some confidence.
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."