Alcaraz felt the discomfort during his victory in the opening match against Finn Otto Virtanen.
It is the second time in three years that the Spaniard has been forced to withdraw from the tournament in Barcelona.
Alcaraz is aiming to win his third straight French Open title at Roland Garros in Paris later this spring. He recently lost the final in Monte Carlo to arch-rival Jannik Sinner, a loss that also saw him demoted from the world number one spot.
