It is the same injury that forced Alcaraz to pull out of this week's Monte Carlo Masters and comes just weeks away from the French Open.
"Despite having tried until the last moment, he will not be in the Barcelona Open," read an organisers' statement.
Alcaraz will set his sights on the Madrid Open - it runs from April 24th to May 5th - which he has also won on the past two occasions.
The 20-year-old is yet to add a French Open crown to his US Open (2022) and Wimbledon titles (2023), his best performance a semi-final last year.
The French Open begins on May 20th.
As top seed in Barcelona, Alcaraz would have had a bye into the second round - a luxury not afforded to his superstar compatriot Rafael Nadal.
The 37-year-old has been given a wild card invite on his return to the ATP Tour for the first time since a hip injury flared up in January.
Nadal plays will play 63rd-ranked Flavio Cobolli of Italy in his opening match.
The 22-time Grand Slam champion has played just once, in an exhibition match against Alcaraz, since his quarter-final defeat by Jordan Thompson in the Brisbane Open.
Nadal missed virtually all of the 2023 season through injury and has dropped to No. 646 in the world rankings.
The injury in Brisbane prompted his withdrawal from the Australian Open as well as Doha and Indian Wells, where he had first intended to make his comeback.
His one appearance since Brisbane came in an exhibition match against Alcaraz in Las Vegas in March where observers noted some discomfort in his back.
With this potentially Nadal's last year on tour, he will be desperate not to miss any more clay court preparation time as he seeks a record-extending 15th French Open title.
"I'm happy to be here, of course, Barcelona is a place that has brought me a great deal of joy, and where I have spent periods of my life," said Nadal at Saturday's draw ceremony.
