The teams have been announced for the Davis Cup finals, which are taking place in Bologna next month.
That is despite the Italians having home advantage for the eight-team knockout, which will happen from November 18-23.
The finals take place just a week after the ATP World Tour finals, the end-of-season tournament between the top-eight ranked players in the world, which will be held in Turin.
Sinner, 24, had to retire mid-match in Shanghai against Talon Griekspoor with severe cramp that he suffered from heat exhaustion.
He won the China Open against American prospect Learner Tien before that, in his first tournament since his four-set defeat by Alcaraz at the US Open final.
Sinner won the Australian Open and Wimbledon this year, reaching the final of all four majors, although he was also beaten by Alcaraz at Roland-Garros.
“Jannik Sinner has not given his availability for 2025,” Italy’s Davis Cup captain Filippo Volandri said.
“The Davis Cup is, and will remain, always his home and I am sure that Jannik will soon be part of the team again. In the meantime, I can count on a group ready to fight and give everything for the blue jersey.”
Italy’s second-highest ranked player, Lorenzo Musetti, the world No8, will lead the team, alongside Matteo Berrettini, the former Wimbledon finalist, lines up alongside Simone Bolelli, Flavio Cobolli, and Andrea Vavassori.
Alcaraz, however, will play alongside Jaume Munar, Pedro Martinez, and Marcel Granollers in the Spain team.
Alexander Zverev, the world No3, will play for Germany.
Davis Cup Finals 2025 full teams
Captain: Paul-Henri Mathieu
Captain: Filippo Volandri
Captain: Michael Kohlmann