Burnley made the announcement on social media at 17:00 GMT, with the game scheduled to kick off at 19:30.
The Premier League said Watford had "an insufficient number of first-team players available to fulfil the match".
It added that the decision was taken "with regret" and apologised for "the inconvenience and disruption caused".
Leicester v Tottenham game on despite both clubs asking for postponement
Reading v Luton & Millwall v Preston postponed
Man Utd players set to return to training after Covid-19 outbreak
'Covid passes' at sport: What does 'Plan B' mean for sport fans in England?
This is the third Premier League match in the last week to have been called off because of Covid outbreaks after Tottenham's trip to Brighton on Sunday and Brentford's home game with Manchester United on Tuesday.
It is also the second time in just over two weeks that a Burnley home match against a London side has been postponed at short notice after Tottenham's trip to Turf Moor was snowed off on 28 November.
The Premier League added: "In considering any application to postpone, the board considers a range of sporting and medical factors.
"Each decision is taken on a case-by-case basis with everyone's health of utmost importance.
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"In light of the recent rise in Covid-19 cases across the country, the Premier League has reintroduced emergency measures. These include protocols such as more frequent testing, wearing face coverings while indoors, observing social distancing and limiting treatment time."
Burnley made the announcement on social media at 17:00 GMT, with the game scheduled to kick off at 19:30.
The Premier League said Watford had "an insufficient number of first-team players available to fulfil the match".
It added that the decision was taken "with regret" and apologised for "the inconvenience and disruption caused".
A statement read: "The Premier League understands this decision will disappoint and frustrate fans who were due to attend this evening's game."
Leicester v Tottenham game on despite both clubs asking for postponement
Reading v Luton & Millwall v Preston postponed
Man Utd players set to return to training after Covid-19 outbreak
'Covid passes' at sport: What does 'Plan B' mean for sport fans in England?
This is the third Premier League match in the last week to have been called off because of Covid outbreaks after Tottenham's trip to Brighton on Sunday and Brentford's home game with Manchester United on Tuesday.
It is also the second time in just over two weeks that a Burnley home match against a London side has been postponed at short notice after Tottenham's trip to Turf Moor was snowed off on 28 November.
The Premier League added: "In considering any application to postpone, the board considers a range of sporting and medical factors.
"Each decision is taken on a case-by-case basis with everyone's health of utmost importance.
ADVERTISEMENT
"In light of the recent rise in Covid-19 cases across the country, the Premier League has reintroduced emergency measures. These include protocols such as more frequent testing, wearing face coverings while indoors, observing social distancing and limiting treatment time."
Burnley made the announcement on social media at 17:00 GMT, with the game scheduled to kick off at 19:30.
The Premier League said Watford had "an insufficient number of first-team players available to fulfil the match".
It added that the decision was taken "with regret" and apologised for "the inconvenience and disruption caused".
A statement read: "The Premier League understands this decision will disappoint and frustrate fans who were due to attend this evening's game."
Leicester v Tottenham game on despite both clubs asking for postponement
Reading v Luton & Millwall v Preston postponed
Man Utd players set to return to training after Covid-19 outbreak
'Covid passes' at sport: What does 'Plan B' mean for sport fans in England?
This is the third Premier League match in the last week to have been called off because of Covid outbreaks after Tottenham's trip to Brighton on Sunday and Brentford's home game with Manchester United on Tuesday.
It is also the second time in just over two weeks that a Burnley home match against a London side has been postponed at short notice after Tottenham's trip to Turf Moor was snowed off on 28 November.
The Premier League added: "In considering any application to postpone, the board considers a range of sporting and medical factors.
"Each decision is taken on a case-by-case basis with everyone's health of utmost importance.
ADVERTISEMENT
"In light of the recent rise in Covid-19 cases across the country, the Premier League has reintroduced emergency measures. These include protocols such as more frequent testing, wearing face coverings while indoors, observing social distancing and limiting treatment time."
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