The former world number one accepted a wild card into the Delray Beach Open and had been due to play his first match next Friday.
Murray’s decision is understood not to be anything concerning regarding his fitness.
He has been given a wild card for the Australian Open and will travel Down Under in mid-January before a period of quarantine prior to the start of the first grand slam of 2021 on February 8.
Australia has strict protocols regarding entry and travelling to the USA first, where coronavirus cases remain high, could potentially jeopardise his plans.
British number one Dan Evans has also pulled out of Delray Beach and the pair will continue to prepare in London ahead of the new season.
Murray defeated Evans and Cameron Norrie at the recent Battle of the Brits event.