Nadal, 32, lost his opening service game and trailed 2-0 in the first set in Paris before recovering well.
He broke Marterer's serve early in the second set and fought back from 3-1 down in the third for a straight-set win against the unseeded 22-year-old.
The Spaniard will play 11th seed Diego Schwartzman, 25, in the last eight.
The Argentine recovered from two sets down to beat South African sixth seed Kevin Anderson 1-6 2-6 7-5 7-6 (7-0) 6-2 to move into the second Grand Slam quarter-final of his career - and first at Roland Garros.
His compatriot Juan Martin del Potro also moved into the last eight with a 6-4 6-4 6-4 win over American ninth seed John Isner.
He will play third seed Marin Cilic, who overcame Italian 18th seed Fabio Fognini 6-4 6-1 3-6 6-7 (4-7) 6-3. The Croat had led by two sets before his opponent played some brilliant tennis, particularly in the tie-break, to draw level.
However, Cilic, who has never progressed beyond the last eight at Roland Garros, broke his opponent in the fifth game of the final set before going on to seal victory.
I don't feel old - Nadal
Nadal, meanwhile, has reached at least the quarter-finals in 12 of the 14 years he has played in the French Open.
The world number one has won 37 consecutive sets in the tournament, though he needed a tie-break in the third set to secure Monday's win over world number 70 Marterer.
Nadal, who celebrated his birthday on Sunday, is now third on the all-time list for most match wins at Grand Slams, moving clear of Jimmy Connors with his 234th.
"I don't feel old, but I am 32, and I have been here since 2003, so it's a long way, a lot of years," said Nadal.
"I started very young. That's a real thing. But, no, I feel happy to be here. I hope to keep doing this for a while."
Schwartzman delight at 'David and Goliath' win
Schwartzman, who is 5ft 7in, said his victory over 6ft 8in Anderson was like "David and Goliath".
"I read it when I was young in school, and I just try to think that when I see Kevin or the guys who are two metres (tall)," he said.
"When you're not as strong or you're not as tall as Anderson, you can still win the match. I think people like me more, as well, for that, because they were supporting me.
"They wanted me to remain in the game and the fact he was twice as tall as me was a reason for me to try and remain. But you can have a very good serve whether you're tall or small. That didn't have anything to do with it."
Nadal, who has won all his five previous meetings with Schwartzman, said of the Argentine: "It's always good to see him in the quarter-final because he's a good friend, a good person.
"He's a worker, and I'm happy to see him having all this success. Hopefully not too much."
French Open: Serena Williams pulls out with injury before Maria Sharapova match
Serena Williams pulled out of the French Open before her fourth-round match with Maria Sharapova because of an injury that affected her serve.
The 23-time Grand Slam winner recently returned to tennis after giving birth to her first child, but looked in good form in her opening matches.
"I've had issues with the right pectoral muscle to the point where I can't serve," said the 36-year-old.
"I'll have a scan. I won't know about Wimbledon until I get the results."
Williams said she first felt the problem during her third-round win over German 11th seed Julia Gorges on Saturday.
She played in a doubles match with sister Venus on Sunday, saying she wanted to try to manage the problem before her match with Sharapova.
"I tried lots of taping and support to see how it felt in match circumstances," Williams said.
"It is hard to play when I can't physically serve. I've never had this injury before, I've never felt it in my life and it was so painful.
"I don't know how to manage it."
Williams said she will have an MRI scan in Paris on Tuesday and will stay in the French capital at least until the extent of her injury is clear.
Sharapova said she was "looking forward" to playing Williams and "disappointed" the American had to withdraw.
"I wish her a speedy recovery and hope she returns to the tour soon," she added.
The 31-year-old Russian, a two-time winner at Roland Garros, will play 2016 champion Garbine Muguruza. The Spaniard was 2-0 up in the opening set of her match against Lesia Tsurenko when the Ukrainian retired hurt.
Rivalry was set to be renewed
The possibility of Williams facing Sharapova had been grabbing attention since the draw was made at Roland Garros 10 days ago.
And the meeting of the two former champions, both making comebacks at Roland Garros this year, was set up when Williams beat Gorges shortly after Sharapova beat Czech sixth seed Karolina Pliskova.
Williams has recently returned after giving birth to daughter Olympia in September, while 28th seed Sharapova is back in the draw after being refused a wildcard last year as she returned from a 15-month drugs ban.
The pair have had a frosty relationship since they first met on court in 2003, although Williams said in her pre-match news conference on Saturday that she did not have any "negative feelings" towards the Russian.
There has not been much of a rivalry on court in recent years, Williams having won 19 of their 21 meetings. Both of Sharapova's wins came in 2004 - including that year's Wimbledon final.
Six matches in six days takes its toll - analysis
Tennis correspondent Russell Fuller at Roland Garros
Williams had been in astoundingly good form in the first week, but footage of the final set of Sunday's doubles - which she and sister Venus lost 6-0 - showed Serena rolling in a number of slow first serves.
The three-time champion chose to play doubles as well as singles because she knew she needed matches under her belt. But six matches in six days - after just four in the previous 16 months - appears to have taken its toll. A pectoral injury is most commonly associated with overuse.
Tuesday's MRI scan will reveal more, but if there is no serious damage, then Wimbledon may still be very much within Williams' sights. There are still four weeks to go, and not being able to play a grass-court warm-up event beforehand should not be a concern: only twice in her career has she done so.
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