De Minaur pulled out of his Wimbledon quarter-final against Novak Djokovic earlier this month after sustaining a cartilage tear in his hip in the fourth round.
"Tried my best to be ready for the singles but body needs a bit more time," he said on Instagram.
De Minaur, who was set to play Germany's Jan-Lennard Struff on Sunday, will be replaced by Portugal's 81st-ranked Francisco Cabral
The Australian will still take part in the doubles alongside Alexei Popyrin. They will meet fourth-seeded U.S. pair Austin Krajicek and Rajeev Ram.
British double Olympic champion Andy Murray also pulled out of the singles tournament to focus on doubles in his last-ever tournament.
Spain's Rafael Nadal, the 22-time Grand Slam champion, was confirmed in the singles draw on Sunday.