Nadal struggled with an abdominal injury during his quarter-final win over Taylor Fritz on Wednesday.
He battled through the pain to win in five sets but is unable to face Kyrgios in their semi-final scheduled for Friday.
Kyrgios will now receive a bye into Sunday's final, where he will face either Novak Djokovic or Britain's Cameron Norrie.
It is the first time the Australian has reached the final of a Grand Slam.
Spanish publication Marca reported on Thursday that Nadal had suffered a 7mm abdominal tear during his win over Fritz.
Announcing his decision to withdraw, Nadal said: "Unfortunately as you can imagine I am here because I have to pull out from the tournament.
"As everyone saw yesterday I have been suffering with a pain in the abdominal and something was not okay there. That is confirmed, I have a tear in the muscle and the communication is too late.
"I was thinking the whole day I was thinking about the decision to make but I think it doesn’t make sense to go, even if I try through my career to keep going.
"It is very tough circumstances but it is obvious if I keep going the injury will be worse and worse."
The official Wimbledon Twitter account confirmed on Thursday that Nadal had pulled out of his match with Kyrgios.
"We're sad to see it end this way, @RafaelNadal," read a tweet.
"Thank you for another year of unforgettable moments at The Championships."
Kyrgios can now look ahead to Sunday's final on Centre Court, where he will face the winner of Friday's other semi-final between Djokovic and Norrie.
No 1 seed Djokovic came from two sets down to beat Italy's Jannik Sinner in his quarter-final, while British No 1 Norrie beat Belgium's David Goffin in five sets in the previous round.
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