Federer and Nadal were set for their 39th meeting, the Spaniard having won 23 times to his great rival's 15, although the Swiss has triumphed in their past five encounters.
Nadal, who has struggled with knee injuries throughout his stellar career, was the second high-profile player to withdraw from the tournament.
Nadal remains without a title since Toronto in August previous year and a win over Federer since the Australian Open in 2017 but with a four-week break he will re-emerge for the clay-court season in Monte Carlo before yet another French Open at Roland Garros. "It's a special rivalry, maybe the most special with Rafa and Novak (Djokovic)".
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"It is not about only today", Nadal said in an emotional press conference after announcing his decision.
Federer has not claimed a Masters title since his Shanghai success over Nadal and the fourth seed has lost just once this season - his fourth round defeat to Stefanos Tsitsipas at the Australian Open. [Nadal] played so well this week and I thought he was playing some of his best tennis again. The trainer returned again with Nadal leading 3-2 in the second set.
Federer, 37, will play either Milos Raonic or Dominic Thiem in the final, bidding for his 101st career title. They've split wins, with Federer winning both of their hardcourt matches and Thiem winning once each on grass and clay.
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"I love to play on hard (courts), but probably my body don't love it that much", Nadal said, according to Christopher Clarey of the New York Times.
"It was an fantastic day", said Thiem, who will be playing in his third Masters 1,000 final.
Knee problems have dogged Nadal for years, and they cut short his 2018 season after the U.S. Open in September. "I warmed up today in the morning, and I felt that my knee was not enough good to compete at the level that I need to compete, to play semi-finals match of this event".
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While Nadal said he feels knee pain "almost always", in the face of this latest setback he insisted: "My goal doesn't change".