The singer tweeted: "We don't create albums with so much care and thought into our track listing for no reason.
"Our art tells a story and our stories should be listened to as we intended. Thank you Spotify for listening."
The streaming service replied "anything for you". A statement later hailed their "new premium feature... to make play the default button on all albums".
A Spotify spokesperson said they were "excited" to be rolling out the feature which was "long requested by both users and artists".
The spokesperson said Spotify users could still choose to shuffle an album, but the system would default to playing tracks in the order chosen by the artist.
"As always, we will continue to iterate our products and features to create the best experiences for both artists and their fans," the statement concluded.
Adele's 30 - her first album in six years - was available on Spotify from its release on Friday.
This marked a change from her last album - 25 - which could only be bought physically or downloaded when it was released in November 2015.
It became the fastest-selling album in British history, shifting more than 800,000 copies in its first week.
It was not until June 2016 that it was made available on streaming sites such as Spotify, Apple Music and Tidal.