Berrettini, who turned 27 on Wednesday, was due to face sixth seed Holger Rune, who advances to the quarter-finals as a result of the Italian's withdrawal and awaits the winner of the match between Daniil Medvedev and Alexander Zverev.
"I don't know where to start...I was finally finding my level and getting back to where I wanted to be... this is a difficult one," Berrettini said in a statement.
"I'm very sad to announce I will not be able to play my match today in Monte Carlo. I felt some pain in my obliques during my match yesterday. The pain became significantly worse overnight.
"After consulting with my medical team we decided to have an MRI scan this morning. I have a grade 2 tear in my internal oblique muscle."
Berrettini has had a tough start to 2023 after being disrupted by a series of niggling injuries towards the end of last year.
The Italian was knocked out of the Australian Open in the first round by Andy Murray and retired in the quarter-finals of his next tournament in Mexico. He was also eliminated in his opening matches at both Indian Wells and Miami.
