Spotify, which earlier gave access to most of the country-pop sensation's back catalogue, on Monday only listed Swift's work on outside projects including the soundtrack to "The Hunger Games."
The music subscription service, in a disappointed but humorous blog post, said that nearly 16 million of Spotify's 40 million users had played Swift's songs in the past month.
"Taylor, 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. It's a love story, baby, just say, Yes," it said, mashing together Swift lyrics.
Spotify offered its users looking for Swift an alternative playlist including suggestively titled songs such as Haim's "If I Could Change Your Mind" and Elvis Presley's "Don't Be Cruel."
Swedish-founded Spotify and competing streaming companies have been a bete noire for many artists and record labels, who charge that musicians earn little revenue and that the services discourage album sales.
On its blog post, Spotify countered that it paid nearly 70 percent of its revenue back to the music world.
"We believe fans should be able to listen to music wherever and whenever they want, and that artists have an absolute right to be paid for their work and protected from piracy," it said.
While Swift's move was sweeping in scope, many major artists have delayed the streaming of new albums so as not to discourage initial sales.
Swift did not immediately comment on the decision but Scott Borchetta, the head of her label Big Machine Records, last year told trade publication Billboard that streaming services were part of a "continued race to the bottom" in devaluing music.
"1989," Swift's fifth album that was released last week, goes firmly in a pop direction and is widely predicted to have the most sales of any new release in 2014 if not in years.
Swift on Monday announced a three-month tour to start on May 20 in the comparatively small community of Bossier City, Louisiana.
Swift will play across North America as well as five dates in Europe three in Britain and one each in Germany and The Netherlands.