The two sides were set to clash at Turf Moor, but snowy conditions forced match officials to postpone the game with the pitch completely covered by the continued downfall.
Antonio Conte's side had arrived in Lancashire for the away game before referee Peter Bankes deemed the conditions unplayable despite the best efforts of Burnley's ground staff to remove the snow.
A Spurs statement read: "We can confirm that today's match against Burnley has been postponed due to adverse weather conditions."
Storm Arwen has swept across the United Kingdom over the weekend.
It remains unclear when the fixture will be rearranged for, with Tottenham next due to host Brentford on Friday (AEDT), while Burnley visits Wolverhampton Wanderers the day before.
Spurs collected their first domestic win under new head coach Conte last time out with a 2-1 win over Leeds United, albeit their good work came undone in a 2-1 reverse on Friday (AEDT) against the UEFA Europa Conference League's lowest-ranked side, NS Mura of Slovenia.