The world No.47, who fell to Novak Djokovic in the decider of the grass-court major earlier this month, was slated to play German Peter Gojowczyk before pulling out on Tuesday local time.
The 2016 champion in Atlanta, Kyrgios, addressed the evening-session crowd after his withdrawal.
"First of all, I just want to say I'm extremely shattered that I'm not able to compete tonight," he said. "I've won this tournament once and I'm playing probably some of the best tennis of my career. All I wanted to do was come out here and give you guys a show, but I'm unable to give my best performance today.
"I'm just extremely sorry, but I'm going to keep my hopes up and maybe be able to continue doubles with Thanasi this week."
Kyrgios and Thanasi Kokkinakis, the reigning Australian Open doubles champions, earned a first-round victory on Monday night against Nicolas Mahut and Edouard Roger-Vasselin.
"I wanted to come out here and see you guys face-to-face to tell you that I love you guys, and hopefully next year in singles hopefully I'll be able to compete and give it my all."