Alcaraz, recently overtaken as world number two by Jannik Sinner, had been due to face Felix Auger-Aliassime in the second round after receiving a first-round bye.
In a statement on X, formerly known as Twitter, the Spaniard posted: “I have been working in Monte Carlo and trying to recover until the last minute from an injured pronator teres in my right arm, but it was not possible and I cannot play!
“I was really looking forward to playing… See you next year”