The match is the fourth in the Premier League to fall victim to the wave of infections sweeping the country, and leaves Spurs with three League games in hand and facing a fixture pile-up in the New Year.
The Premier League board had already rejected requests from both clubs to postpone but the decision is thought to follow a fresh plea from Leicester, who were set to be without 11 senior players.
The postponement request came from Leicester following fresh Covid cases in their squad.
Spurs travelled up on Wednesday and were preparing to play the match.
It follows Watford’s trip to Burnley being called off just two and a half hours before kick-off last night, Manchester United’s game against Brentford being postponed and Sunday’s match between Spurs and Brighton also being called off.
A Premier League statement said: “The Premier League Board has postponed Leicester City FC’s match against Tottenham Hotspur tonight due to an increase in positive COVID-19 cases within Leicester’s squad today,
“In light of the new information, Leicester applied this morning for the fixture to be called off due to an ongoing outbreak within the squad, which has resulted in more players and staff testing positive for COVID-19 today. This has left the club with an insufficient number of players available to fulfil the game.
“Following consultation with the Premier League and UK Health Security Agency, the club’s first team training ground was closed this morning to help contain the outbreak.
“The Premier League understands this decision will disappoint and frustrate fans who were due to attend this evening’s game and apologises for the inconvenience and disruption caused at such short notice.”
Brentford manager Thomas Frank has called for all this weekend’s Premier League fixtures to be postponed.
Leicester boss Brendan Rodgers accused the Premier League board of showing bias towards the club’s rivals and giving undue consideration to TV companies on Wednesday.
“You’re on the right lines [regarding bias],” Rodgers said. “For the integrity of the competition, it’s important, but I’m pretty sure games will have been called off where teams have had less players unavailable than we have.”
Asked whether television contracts had influenced the League’s decisions, Rodgers replied: “I’m pretty sure that’s the case, yes.”