The Spaniard, who spent more than three months out of action due to abdominal and hamstring injuries, returned to the ATP Tour to win the Buenos Aires title by beating Cameron Norrie before losing to the Briton in the Rio final on Sunday.
Alcaraz needed treatment for a left leg problem during his semi-final in Rio and picked up an injury to the other leg against Norrie, leaving him doubtful for his first hardcourt event of 2023.
"I have a grade 1 strain in my right hamstring that will keep me out for several days, according to the tests we did this morning," Alcaraz wrote on Twitter.
"I'm really sad I can't compete here, but now it's time to think about recovering and being ready as soon as possible. I hope to see you all soon!"
Norrie also pulled out of the tournament in Mexico saying he needed to rest.
The Briton, who leads the ATP Tour in match victories this season with 18, is scheduled to return to action at the Indian Wells hardcourt event beginning next week.
"Unfortunately I have to withdraw from Acapulco," Norrie said on Instagram. "It's one of my favourite tournaments, so it's really tough for me to withdraw."
