Wawrinka, who could play Murray in the semi-finals, had to have treatment to his lower back during his 7-5 7-6 (9-7) 6-2 win on Court One, which ended French hopes of a first male champion since 1983.
Throughout their careers, Nadal is 4-2 against Thiem.
That next match will be against the top-ranked Andy Murray on Wednesday.
With a sheepish grin, the eighth seed said: "Actually I'm very bad with the memories". So I was frustrated about it, but I don't know how much impact that had.
Murray went on to say he felt tennis, because of it's global nature, also had the power to unite people from all corners of the world. Previous year he was playing very well and I had to play one of my best matches on clay to win.
"There's a good chance it's a long one".
"Kei is risky off both wings", Murray said. He's tough to play against. And then my second service game I got the warning. Everything is going pretty well just now.
Wawrinka, who claimed the Geneva title just prior to Roland Garros, has now won nine in a row to match his best winning streak on clay. I have hit the ball cleaner and started to see the right shots at the right moments.
Nishikori, a beaten quarterfinalist here in 2015, has now made the last eight of a Slam for a seventh time, a record for a Japanese man.
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Nadal stands two wins from another trophy as title odds improve for the 31-year-old. He was playing better. Now a lot of things are possible. Nishikori doesn't have the mental side.
'I think he's a very good umpire.
"Trying to win tournaments I've never won before is a huge motivation, but I'm not trying to compete with Stan Wawrinka in terms of the numbers", Murray wrote in his BBC Sport column.
The Spaniard has been in ominous form so far and stopping him will take some doing.
On the clay courts of Paris, determined the semifinalists of the 116th version of the Open championship of France. But, yeah, a little bit gained some confidence during second and third.
The incident appear to fire up Murray as the Briton ran away with the second set, but he expressed his dismay at the way the rules are applied.
Although Nishikori cannot remember their NY tussle, he needs no reminding how tough an opponent Murray can be.
"It hasn't always been easy for me here, but these last few years have been great". "We have been playing so many times". Stan this tournament has played great. 3 was very happy about this win: 'For sure I didn't expect that score, but I was confident with my game. I have worked hard to build my confidence.
"Personally I think it was put down to the conditions".
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