The Italian star player suffered an ankle injury while playing against Arthur Rinderknech in the second round of the US Open last year.
Italy will compete in Group A in Bologna against Canada, Chile, and Sweden from September 12 to 17.
Berrettini suffered a grade 2 tear to his internal oblique muscle during the Monte-Carlo Masters.
Berrettini reached the final at the Madrid Masters two years ago when he lost to Alexander Zverev in three sets.
Berrettini’s spot in the draw will be taken by Elias Ymer who is set to face Daniel Altmier.
This win against Zandschulp marked Berrettini’s 19th win in his last 20 grass-court matches.
Matteo Berrettini defeated Andy Murray 6-4, 5-7, 6-3 to win the Boss Open final.
Berrettini announced his decision via social media and claimed that he would delay his comeback to compete in the full grass season.
Berrattini lost the Wimbledon final to World no. 1 Novak Djokovic earlier the same day.
Despite falling behind to Matteo Berrettini, Alexander Zverev claimed his first Masters 1000 title since 2018 in Madrid on Sunday.