The blow comes weeks away from the second Grand Slam of the season, the French Open.
"I felt some pain after playing in Madrid (he lost on Wednesday), some discomfort in my arm," the Spaniard wrote on X, formerly Twitter.
"Unfortunately, I will not be able to play in Rome. I need to rest so I can recover and play 100 percent pain free."
Alcaraz saw his title defence and 14-match winning streak in Madrid come to an with a 4-6, 6-3, 6-2 defeat midweek to Andrey Rublev in the quarter-finals.
He had played for nearly three hours on Tuesday in a three-set win over last year's runner-up Jan-Lennard Struff and felt the effects against Rublev.
"Every time that I'm hitting the forehand, I'm thinking about the forearm, if I'm getting a feeling or not," Alcaraz said after Wednesday's game.
"I have to work hard these days if I want to go to Rome with good feelings, without pain, without thinking about my forearm — but it's going to be a slow process, I guess. I have to be patient in that way."
Alcaraz revealed that he had played with "difficult feelings" towards the end of the match against Rublev, opting to slice his forehand more to put less stress on his forearm.
The French Open, the sole Grand Slam on clay, gets underway on May 26. Alcaraz reached last year's semi-finals.
The two-time Grand Slam champion, who won the US Open in 2022 and Wimbledon last year, turns 21 on Sunday.
