Spotify, the largest site in the fast-growing sector of streaming, made clear that "25," which comes out Friday, would not be available.
"We love and respect Adele, as do her 24 million fans on Spotify. We hope that she will give those fans the opportunity to enjoy '25' on Spotify alongside '19' and '21' very soon," the Swedish company said, referring to the English singer's previous two albums.
Adele's representatives did not immediately comment, nor did rival streaming services, but the singer has given no indication she will offer "25" to Spotify's competitors.
With the move, Adele becomes the most high-profile holdout from streaming since Taylor Swift, who pulled her catalog off Spotify last year as she released her blockbuster album "1989."
Adele's "25" is expected to surpass Swift's album and easily become the biggest in a decade.
Music business journal Billboard, quoting industry sources, said that Adele's label had shipped 3.6 million copies of "25" to retailers.
That would be the biggest number since boy band NSYNC's "No Strings Attached" in 2000, which came out nearly a year before Apple's iTunes shook up the industry by mainstreaming digital sales.
Adele has already broken the record for first week downloads with the album's initial song, the ballad "Hello."
"21," Adele's previous album which came out in 2011, became an international sensation in part through the popularity of the heartache song "Someone Like You."
"21" was the top-selling album in the United States for two consecutive years and remains comfortably the biggest release in Britain so far this century.
Streaming - which allows unlimited, on-demand music online - has grown rapidly in the past several years despite criticism from some artists who say the payouts are too low.
Swift earlier this year changed course and put her tunes on Apple Music, the new streaming service of the tech giant, after it complied with her call to improve the payout structure for artists.