The World No 2 was last in action on Tuesday at the ATP 500 event, where he beat Otto Virtanen 6â-4, 6â-2 in his opening-round match. Despite the straight-sets victory, Alcaraz appeared visibly troubled by wrist discomfort towards the end of the first set.
He subsequently skipped practice the following day before making the decision to pull out of the tournament.
Alcaraz had been due to compete at the Madrid Open, scheduled from 22 April to 3 May, but has now also withdrawn from that event as he continues his recovery.
"There are some pieces of news that are very difficult to share," said the six-time Grand Slam champion in a post on Instagram.
"Madrid is like home to me - one of the most special stops on the calendar - and that's why it hurts so much not to be able to play here for the second year in a row.
"It's especially painful not to be there in front of my fans at such an important tournament. Thank you, as always, for your support, and I hope to see you all again soon."
The Spaniard also skipped the event in the Spanish capital last season, due to right leg abductor discomfort.
Less than 48 hours prior to his Barcelona Open first round, Alcaraz had suffered a 7-6(5), 6-3 loss to Jannik Sinner in the final of the Monte Carlo Masters.
As a result, the Spaniard lost the world No 1 spot for the first time since mid-2025.
Alcaraz immediately flew to the ATP 500 event and looked set on attempting to capture his third title in Barcelona.