Top seed Medvedev, who plays on Thursday for a quarter-final spot against Denis Shapovalov, can tighten his grip on his current top position heading into the US Open.
The 36-year-old Spaniard, who won the Cincinnati title in 2013, was playing his first match in well over a month after withdrawing with an abdominal injury from his Wimbledon semi-final.
Spain will instead be looking to teenage sensation Carlos Alcaraz for inspiration.
The announcement marks a major blow to the Spaniard's hopes of being fully fit for the US Open which begins in New York at the end of the month.
Nadal owns a men's-record 22 Grand Slam titles, two ahead of Djokovic, who is 35, and Federer. "It's going to be a sad day," Kyrgios said, "when they go."
The 22-time Grand Slam champion has an abdominal injury and says he won't play his semifinal match against Nick Kyrgios on Friday.
The 36-year-old said he was unsure over his ongoing participation in the tournament as he targets the third leg of a rare calendar Grand Slam.
He did complete it, but said he couldn't be sure whether he will be able to play on Friday against Nick Kyrgios.
Williams was far below her imperious best on Tuesday, struggling from the start with her form and fitness.
There has been more variety among the women's title winners lately, with seven players dividing the past eight Wimbledon trophies.
Djokovic is bidding for a seventh title at the All England Club to move level with US great Pete Sampras.
The seedings for Wimbledon were announced on Tuesday, with Djokovic and Nadal being Nos. 1 and 2, respectively, in the men's draw because of the absence of Daniil Medvedev and Alexander Zverev.
Nadal, who confirmed he was going to be a father for the first time, travelled to Barcelona last week to begin "pulsed radiofrequency stimulation", a treatment aimed at reducing nerve pain.
Rafael Nadal's status for Wimbledon is in doubt because of a chronic problem with his left foot — as is his future in tennis.
Before continuing his grass court preparations, Andy Murray did the maths on Rafael Nadal's latest feat on clay.
The 14th French Open title and his 22nd Grand Slam crown helped Rafael Nadal move up a place from fifth to fourth in the latest ATP Rankings released.
Nadal, the oldest ever champion in Paris at 36, now has 112 match wins on the famous crushed red brick against just three defeats in 17 years.
More than three hours in, Rafael Nadal and Alexander Zverev had only finished 23 games and a tie-break.
Nadal's victory came two days after his 36th birthday and made him the oldest title winner in the history of the clay-court tournament.
Rafael Nadal will become the oldest man to win the French Open title if he defeats Casper Ruud, the Norwegian whose clay court talents he has personally helped foster.