The Clarets were due to take on the Hornets in midweek, but a high number of COVID-19 cases within the Burnley squad mean the game cannot go ahead.
Manager Sean Dyche recently suggested he only had 10 first-team players available for training.
A Premier League statement included an apology "for the inconvenience and disruption caused to supporters who would have attended or watched the game".
The statement also added: "We are fully aware that postponements disappoint clubs and fans."
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