Adele, 27, is thought to have followed in the steps of Taylor Swift and made the decision not to put her music on the services.
Spotify says it hopes Adele will change her mind “very soon”.
However, fans can buy 25 in music stores and on sites like iTunes and Amazon.
Adele’s previous albums 19 and 21 as well as her current single Hello are still available for streaming.
The singer is said to be one of the few superstars who has enough influence to decide how she wants people to listen to her music.
A statement from Spotify said: “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 new album is not available to stream on Apple Music, but Apple said it was “thrilled” to offer it for download on iTunes.
Another artist who made the same decision as Adele was Taylor Swift, who pulled her music from Spotify in 2014 following a row over the royalties paid by streaming outlets.
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