The decision comes a week after the Clarets boss Sean Dyche tested positive for Covid.
The Premier League accepted a request lodged by Burnley, who were already without several players through Covid-19, injuries and Maxwel Cornet’s absence at the Africa Cup of Nations prior to the enforced sale of Chris Wood to relegation rivals Newcastle this week.
The game against Leicester City which was set to take place on Saturday 15 January, will now be rearranged for a later date.
The club are currently 18th in the Premier League and under-threat of relegation.
A statement from The Clarets said: "Burnley Football Club can confirm that our Premier League fixture at home to Leicester City on Saturday 15th January has been postponed.
"The Club submitted a postponement application which was approved by the Premier League Board due to a number of injuries and Covid-19 cases within the first team squad.
"The Premier League fixture between Burnley and Leicester City at Turf Moor will now be rearranged for a future date, with all previously purchased tickets for the game to remain valid.
"The Club sends their apologies to both sets of supporters for the inconvenience this may have caused and a new date for the fixture will be confirmed in due course."
Listen to ITV News' coronavirus podcast.