Italy captain Filippo Volandri announced on Saturday that Sinner, who will contest the US Open men's singles final against American Taylor Fritz, would be rested for the Cup finals.
"As far as Jannik goes, who told us he was available for the latter stages of the competition in Bologna, in accordance with the federation leaders and his staff, we decided to relieve him of his call-up and allow him a full recovery," Volandri said in a team announcement.
The top-ranked Sinner was exonerated in a doping case less than a week before the US Open began.
With Sinner missing, defending champions Italy will instead be composed of Matteo Berrettini, Matteo Arnaldi, Flavio Cobolli, Andrea Vavassori and Simone Bolelli.
Olympic bronze medalist Lorenzo Musetti also needs rest and asked not to play, Volandri said.
Sinner led Italy to the Davis Cup title last year, posting wins over Novak Djokovic in both singles and doubles in the semi-finals against Serbia, then earning the decisive point in the final against Australia by beating Alex de Minaur.
Italy open against Brazil on Wednesday (local time), then face Belgium on Friday and the Netherlands on Sunday.
Group play will also be contested in Valencia, Spain; Zhuhai, China; and Manchester, England.
The top two teams in each group will advance to the final eight in Malaga, Spain, from November 19-24.
Sinner was widely criticised when he opted out of the group phase in Bologna last year. The criticism was then quickly drowned out by praise when he led Italy to the title and then won his first grand slam trophy at the Australian Open in January.
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