Williams announced her withdrawal at a news conference at Roland Garros on Monday.
The 10-time former champion has won in straight sets against Richard Gasquet 6-3, 6-2, 6-2.
The crowd performs a wave as Spain's Rafael Nadal plays France's Richard Gasquet during their third round match of the French Open tennis tournament at the Roland Garros stadium, Saturday, June 2, 2018 in Paris.
"Of course I have won a lot, and it can maybe influence my opponents".
Given his imperious record against Gasquet, Nadal will not feel he needs to adapt his style of play so expect more of the same baseline dominance from the world number one.More news: Gmail's major redesign will be available to all in July
"I played very well, I'm sorry for Richard, he is a good friend and a good person", said Nadal, who played a few rallies with a ball boy after his match. "It has been three hard matches for me, but I played well and I know I could play even better in my next round", del Potro said.
As is customary after a win, the player was interviewed by a court side presenter.
Nadal, whose birthday is on Sunday, is to play his 40th career round-of-16 match at a major against Germany's Maximilian Marterer, who defeated Estonia's Jurgen Zopp 6-2, 6-1, 6-4.
Croatia's Marin Cilic, the third seed, came through with no fuss 6-3 6-2 6-4 against American Steve Johnson.
Diego Schwartzman joined countryman del Potro in the fourth round with an impressive 7-5, 6-3, 6-3 victory over Borna Coric. Juan Martin del Potro was a victor over former quarterfinalist ALbert Ramos Vinolas 7-5, 6-4, 6-1.More news: Miss America Will No Longer Include Swimsuit Competition
In another rain-affected game, Belgian David Goffin (8th seed) saved four match points to defeat Frenchman Monfils in a thriller, 6-7 (6) 6-3 4-6 7-5 6-3.
The 64th-ranked Mischa lost in the third round to 2017 US Open runner-up Kevin Anderson 6-1, 6-7 (3), 6-3, 7-6 (4) on Saturday. "Do you mind just playing one ball with him?" Alexander Zverev and Karen Khachanov will battle for a first Grand Slam quarterfinal and Goffin returns to face the surprise Marco Cecchinato.
Djokovic has been shaky at times, too.
Should he and Fognini, who is also through to the round of 16 this year, both reach the quarterfinals, it will be the 2nd time in the Open Era that Italy has had multiple representatives in the quarterfinals of the men's singles at a Grand Slam.
Unseeded Karen Khachanov of Russian Federation has reached the French Open's round of 16 for the second consecutive year, eliminating 15th-seeded Lucas Pouille of France 6-3, 7-5, 6-3 in the resumption of a suspended match.More news: Apple focuses on speed, parental controls in software upgrades