In an open letter to Apple, Swift said she was withholding the record as she was unhappy with the three-month free trial offered to subscribers.
"I'm not sure you know that Apple Music will not be paying writers, producers, or artists for those three months," she wrote.
She said the plan was "unfair", arguing Apple had the money to cover the cost.
"I find it to be shocking, disappointing, and completely unlike this historically progressive and generous company," the 25-year-old said, describing Apple as one of her "best partners in selling music".
"These are not the complaints of a spoiled, petulant child. These are the echoed sentiments of every artist, writer and producer in my social circles who are afraid to speak up publicly because we admire and respect Apple so much," she continued.
"We know how astronomically successful Apple has been and we know that this incredible company has the money to pay artists, writers and producers for the 3 month trial period - even if it is free for the fans trying it out.
"Three months is a long time to go unpaid, and it is unfair to ask anyone to work for nothing."
She ended her letter by calling on Apple to change its policy, suggesting she would reinstate her album on the service if the company changed its mind.
"We don't ask you for free iPhones. Please don't ask us to provide you with our music for no compensation."
Apple has yet to comment on the issue.
The rest of Swift's back catalogue will remain available on Apple Music when it launches on 30 June. It will cost $9.99 (Â£6.30) per month in the US for one person or $14.99 for families.
The music industry has generally supported the company bringing its vast music library to paid streaming, and the company said it will pay 70% of the music subscription revenue to music owners.
It is not the first time Swift has spoken out against streaming music - she pulled her entire catalogue from Spotify last November and had refused to offer 1989 on streaming services, saying the business had "shrunk the numbers of paid album sales drastically".
1989 went on to become one of the biggest-selling albums of 2014 and has sold more than 4.9 million copies in the US alone.
Last week, UK-based independent record label Beggars echoed Swift's comments, saying it struggled "to see why rights owners and artists should bear this aspect of Apple's customer acquisition costs".
It said it did not have an agreement with Apple that would allow it to participate in the new service but hoped the "obstacles to agreement can be removed" in the coming days.

Police said the Bolton man was riding a BMW motorbike when it collided with a Citroen car driven by a local man on Hailwood's Rise on the (A18) Mountain Road at 06:45 BST.
The rider was treated at the scene but was pronounced dead on arrival at Noble's Hospital.
Both vehicles were travelling in the direction of Douglas.
Insp Dave Dobbie said it was a "very sad outcome".
Police closed the road for four hours following the crash and are appealing for witnesses.
Taylor Swift has pulled her hit album 1989 from Apple's new streaming music service and criticised the company.
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A 55-year-old motorcyclist from Greater Manchester has been killed in a crash involving a car on the Isle of Man.