Spaniard Nadal, 31, beat his 31-year-old opponent 6-3 6-7 (5-7) 6-3 and faces Serbian qualifier Filip Krajinovic, 25, in the last eight.
Paris Masters tournament director Guy Forget acknowledged Nadal's withdrawal was a serious blow to an event often hit by late retirements at the end of the season, and said that the Spaniard's participation in the Tour finals was unlikely. But unfortunately it was impossible for me to return to the court in the same condition as last night.
Although in 2017 Wimbledon, he was out after a defeat by Luxembourg ace Gilles Müller in the round of 16, Nadal clinched his fourth US Open trophy after the win over South Africa's Kevin Anderson.
But he allayed fears this fresh setback would lead to another lengthy spell on the sidelines. It's something that means a lot to me.
He added: "The way that I am today I do not see myself playing three more matches". It's normal that these kind of things happen. "The knee is always bothering a little bit but sometimes it's worse".
Top seed Nadal, a victor of 16 Grand Slam titles, had his knee heavily strapped in a battling three-set win against Uruguay's Pablo Cuevas yesterday.More news: Uzbekistan president offers help in NY truck attack investigations
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If Nadal pulls out of the Tour Finals, it would leave Federer as the only member of the "Big Four" in the year-ending event for the first time since 2005.
"I am going to do my treatment and my best to be playing in London".
"For me it's not about London".
"It's not about London, it's about the longer term", he emphasised.
Nadal said that "the pain during the match (on Thursday) was too much".