The 20-year-old two-time Grand Slam champion won the tournament in 2022 and 2023. He has taken one title this year, at Indian Wells last month.
"(Alcaraz) has suffered from the injury sustained in Monte Carlo, and did not have a good feeling in his training on Sunday and, despite having tried until the last moment, he will not be in the Barcelona Open," organisers said on social media platform X.
The main draw of the Barcelona Open starts on Monday, with the tournament concluding next Sunday.