Alcaraz, a seven-time Grand Slam champion, was scheduled to play the Italian, but Berrettini pulled out ahead of their encounter with an elbow injury.
"Unfortunately, the pain in my arm that I've been putting up with for the past few days means I won't be able to take to the court tonight," Berrettini posted on social media.
After receiving a bye through the first round as a top-eight seed, Alcaraz is into the last eight with only one match under his belt in Paris, a straight-sets success against Alex Michelsen.
He will meet American Taylor Fritz on Friday for a spot in the semi-finals. Fritz beat French sixth seed Arthur Fils 6-3, 6-4 to stay in the running for a place at the ATP Finals.
Alcaraz has never won the Paris Masters. The Spaniard is the top-ranked player remaining in the draw after world number one Alexander Zverev lost on Wednesday.
Berrettini, 30, has endured an injury-plagued career and was forced to retire earlier this season in Paris when a hip issue brought a premature end to his French Open quarter-final clash with Matteo Arnaldi.
Shelton sets up Paul clash
Ben Shelton overcame France's Arthur Rinderknech in a third-set tie-break to secure his passage into the quarter-finals.
The American third seed battled past the 68th-ranked Frenchman 6-3, 4-6, 7-6(5) to avoid becoming the latest high-profile departure.
Shelton will next play compatriot Tommy Paul after the 12th seed beat Frenchman Quentin Halys 7-6(3), 6-4 in the day's opening match on centre court.
"It's been a long time since we've been on the court, but I'm looking forward to it," Shelton said of taking on Paul for the first time since losing to the world number 14 in Dallas two years ago.
"He's in great form right now. A great player, a great friend."
Australian qualifier Rinky Hijikata continued his run as he backed up his second-round victory over 24-time major champion Novak Djokovic with a 2-6, 6-3, 7-5 win against Tomas Martin Etcheverry.
Zverev's vanquisher Lorenzo Musetti, however, failed to use his round-of-32 upset as a springboard to a first 1000-level title, losing a long three-set battle to Frenchman Luca Van Assche.
Former world number two Casper Ruud of Norway overcame Germany's Jan-Lennard Struff in the late match, winning 6-3, 6-3 to complete the quarter-final bracket, where he will take on Nuno Borges of Portugal.
The tournament lost a swathe of top seeds on an upset-filled Wednesday as Daniil Medvedev, Frances Tiafoe and Alex de Minaur all joined Zverev and Djokovic in exiting early.
