The world's third-ranked tennis player felt an injury in his left leg already during the final in Barcelona on Sunday, the Spaniard lost to the Dane Holger Rune.
Alcaraz was supposed to enter the tournament in Madrid, which he has won twice and where he was seeded second this year, on Sunday, but is now choosing not to play.
A tough decision, Madrid is one of the tournaments that is extra special for me. It was one of the first I watched as a boy.
Sometimes you have to think about your health and what's important. A Grand Slam is a Grand Slam. If I play here, I risk aggravating the injury and maybe not being able to play for several months. It's not worth it, says the Spaniard.
Alcaraz is the reigning champion on Roland Garros. In last year's final, he defeated the German Alexander Zverev.
If the rest and rehabilitation go as planned, Alcaraz hopes to be able to play the clay court tournament in Rome as the last preparation before this year's second Grand Slam.