Covid-19 cases within the Everton camp had seen the Merseysiders request a postponement.
But that initial plea was rejected despite Everton manager Rafael Benitez saying he only had nine fit outfield players at his disposal for the fixture on Boxing Day, traditionally one of the busiest days in the English football calendar.
Everton, however, said Friday that the game had been called off, with a club statement saying: "Our Premier League fixture at Burnley on Boxing Day has been postponed due to the number of COVID cases and injuries in our squad."
The Premier League added it had taken the "regrettable" decision to postpone the game following a board meeting on Friday.
"The board reviewed the club's request today to postpone the match following further injuries to their squad.