De Minaur made a run to the US Open quarter-finals but was hampered by the hip as he exited the Grand Slam in a straight sets defeat by Briton Jack Draper.
Australia captain Lleyton Hewitt confirmed the world number 11 was sidelined ahead of their opener against France in Valencia later on Tuesday.
"Alex has done some incredible stuff in Davis Cup over the last three or four years now," said Hewitt.
"But he's been battling since Wimbledon and he's hasn't really been close to 100%. He was desperate to play, but in the end it really wasn't much of a choice."
Hewitt said Australia, also pooled with the Czech Republic and Spain, were in an "awfully tough group".
However, he was confident his team could progress without De Minaur, pointing to the form of players at the US Open.
Alexei Popyrin upset Novak Djokovic at Flushing Meadows to reach the last 16, while Jordan Thompson and Max Purcell combined to win the men's doubles.
"We back ourselves against anyone," he said.
"These guys put in the hard yards, not just this week leading into this tie, but throughout the year. They'll be full of confidence when we start."
Australia, the second most successful nation in Davis Cup behind the United States, reached the finals of the last two tournaments, losing to Italy last year and Canada in 2022.
Australia won the last of their 28 titles in 2003, with Hewitt winning a singles rubber to help beat Spain in the Melbourne decider.
