The seven-time Grand Slam champion was scheduled to play the Italian in the last 16, but Berrettini pulled out ahead of their encounter due to 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 due to being a top-eight seed, Alcaraz is now into the last eight with only one match under his belt in Paris.
He will meet either Arthur Fils or Taylor Fritz on Friday for a spot in the semi-finals.
The Spaniard has never won the Paris Masters, and is the top-ranked player remaining in the draw this year 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.
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 (7/5) 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 (7/3), 6-4 in the day's opening match on centre court.
With Alcaraz no longer on the menu, local player Fils will headline the night session later when the world number seven faces off against American 11th seed Fritz.
Former world number two Casper Ruud of Norway will also be in action against Germany's Jan-Lennard Struff.
The Paris Masters lost a spate of top seeds on an upset-filled Wednesday as 24-time major champion Novak Djokovic, Daniil Medvedev, Frances Tiafoe and Alex de Minaur all joined Zverev in exiting early.