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 was set to play Germany's Jan-Lennard Struff on Sunday.
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.