Spotify has stopped streaming Taylor Swift's music at her request, setting up a business struggle between the leading provider of a new music distribution system and the industry's most popular artist.

The music streaming service sounded like a spurned boyfriend in a statement announcing the split. It said Taylor's management told it to pull the music late last week and it was done yesterday, so all her songs were no longer available to its 40 million users.

"We were both young when we first saw you, but now there's more than 40 million of us who want you to stay, stay, stay," Spotify said. "It's a love story, baby. Just say yes."

Taylor's single Shake It Off was the most-played song on Spotify last week.

The decision means that a large number of fans will have only one option to hear her new album, 1989, and that is to buy it, which hundreds of thousands of people have already done. Music's most influential artist is simultaneously making a political statement and a savvy business move.

More than 700,000 people bought 1989 in the first two days it went on sale last week, according to Nielsen SoundScan. That already exceeds the year's biggest one-week seller, Coldplay's Ghost Stories, which sold 383,000 in May.

Nielsen music analyst David Bakula said Taylor, 24, who has announced that she will launch a world tour next year, is on target to challenge the 1.2 million copies she sold the first week her last album, Red, went on sale.

Music streaming services and file sharing have sharply cut into music sales for artists over the past couple of years. Many artists complain that the fees Spotify pays to record labels and music publishers, with a portion eventually funnelled to musicians, is too small.

The 1989 album has never streamed on Spotify, although Shake It Off was allowed on the service. All of the music Taylor has officially released in her career, including Shake It Off, was pulled yesterday.

Taylor's move has precedence. She briefly pulled Red from Spotify around the time that album came out, although she did not remove her entire catalogue and Red eventually appeared on Spotify. This summer, Taylor wrote in the Wall Street Journal that artists should fight to be paid what they were worth.

"Music is art, and art is important and rare," she wrote. "Important, rare things are valuable. Valuable things should be paid for. It's my opinion that music should not be free and my prediction is that individual artists and their labels will someday decide what an album's price point is. I hope they don't underestimate themselves or undervalue their art."

Spotify says nearly 70% of the revenue it receives from paying customers goes back to rights-holders in the form of royalty payments and the more people who pay for Spotify the more money artists get. People pay 9.99 dollars (£6.28) a month for Spotify's premium streaming service.

But artists are getting more vocal in their complaints about how music streaming is damaging their ability to make a living. In a Facebook post this autumn singer Rosanne Cash called music streaming "dressed-up piracy".

"I'm in this business and I see young musicians give up their missions and dreams all the time because they can't make a living," she wrote. "Someone has to speak up for them."

It is unclear whether Taylor's move will start a trend with other musicians, many of whom might not want to risk cutting their fans off from a way of hearing music that is growing increasingly popular.

It is similar to when several artists were reluctant to let their music become available on iTunes when that service started, although most eventually came around, said Keith Caulfield, associate director of charts and sales at Billboard magazine.

Taylor "is in a fairly unique situation", he said.

Veteran rocker Holly Johnson said it was only pop's giants who could afford to follow in Swift's footsteps.

Johnson, best known as lead vocalist for Frankie Goes to Hollywood, said: "I think ten years ago I was saying, well, you had to be on iTunes if you wanted to exist in pop music and now I feel the same way about Spotify ... only the very biggest and most successful artists can afford not to be on it."

Swift has previously spoken of her belief that artists' work must not be undervalued.

"Music is art, and art is important and rare. Important, rare things are valuable. Valuable things should be paid for," she wrote in the Wall Street Journal in July, though she did not specifically refer to the royalty rates paid out by Spotify and other streaming services to artists and their representatives.

Craig Reid, from Scottish duo The Proclaimers, said he agreed artists should be paid their worth - in principle.

"(But), as Bono said, it's only really honest people and little girls that pay for records nowadays," he said today.