Kyrgios was leading 4-1 in the first set when his shoulder started playing up, hampering his blistering serve, the most lethal weapon in his arsenal.
"There's no point for me to play if I can't really serve, because serving is my strength, my favourite shot," the Australian sixth seed, who also withdrew from last weekend's Laver Cup with the same injury, told reporters.
"So if I'm not able to serve at my best and I'm hindered, I'm probably not going to bother playing until I can get it right again.
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"I was playing well in the first set, I was obviously up a break serving for the set and... I was obviously struggling a lot. I'm serving usually somewhere around the 230 km per hour(143mph) mark and I wasn't even able to crack about 180."
Kyrgios, whose fiery temperament has often landed him in trouble with tennis authorities, said he would consider resting until the Davis Cup finals in Madrid in November.
Australia have been drawn in Group D, alongside Belgium and Colombia.
"I want to play (in the) Davis Cup toward the end of the year, that's mid November. So until ... then I've got a lot of time, I can rest, recover, get my shoulder right," Kyrgios added.
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