Djokovic, chasing a third Roland Garros championship and a 23rd men’s Grand Slam title, beat 94th-ranked Peruvian opponent Juan Pablo Varillas 6-3, 6-2, 6-2.
The 36-year-old Serb, champion in Paris in 2016 and 2021, will face the 11th seed Karen Khachanov for a place in the semi-finals.
Djokovic is one of the favorites to win the French Open this year with 14-time champion Nadal sidelined for the first time since 2004 after failing to recover from a hip injury.
On Saturday, his 37th birthday, it was revealed that Nadal would need at least five months of rehabilitation following keyhole surgery on his injured hip.
That means he probably won’t play again until 2024, which will be his last season on tour.
“I really hope his rehabilitation process goes well and we can see him next season,” Djokovic said of Nadal who he faced 59 times in his career.
He and the Spaniard are tied on 22 Grand Slam titles.
“He is so important to our game on and off the court, one of the greatest legends in tennis. We want to see healthy Rafa, without a doubt, playing for what he announced his last season. J hope he can do this.”
On his record 17th quarter-final in Paris, and 14th in a row, Djokovic added: “I’m very proud of this record. I put a lot of effort into my game and I’m very motivated to continue. “
“However, my attention is already on the next game. I know what my goal is here. I try to mentally stay on course and not look too far ahead.”
Djokovic holds an 8-1 career lead over Khachanov, including their only previous meeting at Roland Garros in 2020.
The Russian reached the quarter-finals for the second time with a 1-6, 6-4, 7-6 (9/7), 6-1 victory against Lorenzo Sonego from Italy.
Khachanov, 27, hopes his penchant for chess will help him in his strategic and tactical battle with Djokovic on Tuesday.
“You have to play chess really well to beat him,” Khachanov said.
“I like to play chess in the morning to get the brain working. I think there are some similarities here.
“I think when you open your head up and you’re really into the game, you see the pitch a lot bigger. You see the possible shots that you can cause problems for the opponent. I think there’s has similarities. Maybe that helps me.”