Berrettini pulled out of the Monte Carlo Masters with pain last week and it later turned out he had suffered a tear in an oblique muscle.
"The intense rehab program has begun with my medical team in Barcelona," Berrettini wrote on Instagram.
"I will do everything I can to be back competing as soon as possible. Unfortunately I will not be able to compete in Madrid. I will keep you all updated when I have more news."
The Madrid open will be played in the Spanish capital from April 25th to May 7th.