The Team GB star was champion at London 2012 and Rio 2016, becoming the first player to ever defend a singles title in tennis.
Murray was due to start his campaign against Canada's Felix Auger-Aliassime on Sunday but after consulting with medical staff he was told not to compete in both the singles and doubles.
The three-time grand slam winner started his doubles campaign alongside Joe Salisbury with an upset win over second seeds Nicolas Mahut and Pierre-Hugues Herbert on Saturday.
Murray will continue his quest for a third Olympics gold alongside Salisbury.
"I am really disappointed at having to withdraw but the medical staff have advised me against playing in both events," Murray said.
"So, I have made the difficult decision to withdraw from the singles and focus on playing doubles with Joe."
Murray was considered an outsider for singles success in Tokyo having been blighted by injuries in recent years.
His absence is a blow to a men's singles event already missing the likes of Roger Federer, Rafael Nadal and Dominic Thiem, though.
World No.1 Novak Djokovic is the overwhelming favourite to win gold. The Serbian has already won the Australian Open, French Open and Wimbledon in 2021 and is chasing Olympic gold and the US open to become just the second player after Steffi Graf to complete the coveted 'Golden Slam'.