Users can flick through the animated visuals and text directly in the app as they would on an e-reader device, and in the same way they currently interact with the stories of those they follow.
The library enlisted New York-based advertising and creative agency Mother for the branding, and to source artists and designers who could create colourful visuals to accompany each title.
The aim is "to make some of the world's most classic pieces of literature more accessible to the masses", according to a statement from Mother and NYPL.
Insta Novels launched today with Lewis Carroll's Alice in Wonderland and dynamic graphics by designer Magoz.
It begins with a blonde girl in a blue dress walking towards an eye-like design, which then transforms into a moving clock.
Eventually, the images are replaced with the text, which is laid out like a typical book page with numbers in the top right corner.
To the bottom right, a space is reserved for the reader to place their thumb, which pauses the story so they can peruse at their own pace.
"Instagram unknowingly created the perfect bookshelf for this new kind of online novel," added Mother partner and chief creative officer Corinna Falusi.
"From the way you turn the pages, to where you rest your thumb while reading, the experience is already unmistakably like reading a paperback novel."
Backgrounds on the text pages are coloured warm white, rather than the typical bright blue-white of smartphone screens, to be easier on the eyes.
The Georgia typeface was selected because it "pays homage to the history of the written word in both print and digital", said the statement. "It was one of the first serif fonts ever designed for the screen to make long-form text more pleasing and legible."
Instagram story posts are typically only viewable for 24 hours after they are uploaded. But NYPL has added the Alice in Wonderland pages to its "highlights", which works like an archive, and can be accessed from its page at any time.
In the coming months, the library will post two more Insta Novels. The Yellow Wallpaper by Charlotte Perkins Gilman will be illustrated by Buck, and The Metamorphosis by Franz Kafka will feature graphics by César Pelizer.
Monday worked with designers who already had a significant presence on Instagram, in order to help promote the initiative.
NYPL hopes that Insta Novel readers will also download its e-reader app SimplyE to continue reading more stories on their smartphones.
The library offers an extensive e-book collection available for borrowing, for those registered with its system. Members must be residents of New York City.
"This project is directly in line with the library's mission is to make the world's knowledge accessible to all," said NYPL chief of external relations Carrie Welch.
Previous initiatives to get New Yorkers to read more have included a "virtual library shelf" installed on subway trains, which allowed passengers to browse the first 10 pages of a book on their smartphones, before directing them to the nearest library to pick up a hard copy.
Visuals are by Mother.