Patrons streamed toward the returns desk at the Brooklyn Public Library’s main branch on Friday afternoon, buzzing with excitement. Several posed for pictures in the building’s lobby, which was newly plastered with images of Jay-Z, then signed up for special library cards that feature artwork from the rapper’s albums.

The limited-edition library cards are the marquee souvenir from “The Book of Hov,” an exhibition honoring Jay-Z that took over the library last month.

The cards are free for New York State residents and are available at Brooklyn Public Library branches in 13 different designs, each featuring the cover art from one of Jay-Z’s solo albums. Fans, who see the cards as instantly classic pieces of hip-hop memorabilia, are tracking them down with the sort of fervor usually reserved for vinyl records or concert tees.

“Jay-Z being a Brooklyn native, he goes hard for Brooklyn, and his fans go hard for him,” said Chaz Barracks, 35, an artist and postdoctoral fellow at Syracuse University. He had taken a five-hour bus ride to Brooklyn to visit the library. “The card was worth it,” he added.

According to the library, 11,000 new accounts have been created with associated Jay-Z cards. Branches that offered the limited-edition cards recorded a more than 1,000 percent increase in registrations in the last two weeks of July over the same period in June.

Linda E. Johnson, the Brooklyn Public Library’s chief executive, said she had proposed a limited-edition card early in the library’s conversations with Roc Nation, Jay-Z’s entertainment company, which created the exhibition. The library had previously released cards featuring the work of Maurice Sendak, the author and illustrator of “Where the Wild Things Are.”

“Swag in the form of T-shirts or mugs, that’s not really what we’re about,” Ms. Johnson said. “The card is your ticket to everything we have.”

Roc Nation came back with the suggestion that they make 13 cards instead. The library decided to allow patrons to collect one of each style, but to rotate different card designs through many of the library’s branches to encourage fans to visit several locations.

That plan appears to have worked, with some Brooklyn residents rushing out to collect the set of cards “like Pokémon,” as one social media user described it. Olayinka Martins, 26, a writer living in Brooklyn, spent three days visiting nine different branches in order to collect all 13.

Mr. Martins, who learned to read through the Brooklyn library system, said he thought it was smart to plug into the hype cycle that exists around hip-hop merchandise. “The library leadership understands that hip-hop and Black culture have been the site of cool, and cool sells,” he said. “It’s very savvy.”

The cards have caught the attention of Jay-Z fans outside the state, who cannot register for them because they lack New York addresses. Online, some are begging New Yorkers to mail them the cards. Complete sets are listed on eBay for upward of $1,000.

Mr. Martins did not collect the cards planning to sell them, but he said he had been tempted by offers of more than $700.

Ms. Johnson said the library had not been surprised to learn that people were trying to resell the cards. “We wish they weren’t doing it,” she said, “but it’s a small enough number that we’re not so worried right now.”

The Brooklyn Public Library is just one of several New York City institutions recognizing the 50th anniversary of hip-hop, which had its origins in the South Bronx. The Metropolitan Transportation Authority has released four MetroCards honoring LL Cool J, Pop Smoke, Rakim and Cam’ron, which are being sold near each of the artists’ birthplaces. And the New York Public Library, which has locations in Manhattan, the Bronx and Staten Island, has released a special-edition card featuring imagery from the cassette that accompanied the 1983 film “Wild Style.”

Brooklyn residents have been especially excited by the Jay-Z exhibition, which traces the artist’s life from his childhood in the Marcy Houses, a public housing complex in the Bedford-Stuyvesant neighborhood of Brooklyn, to his career as a musician and mogul.

Olivia Shalhoup, 26, who runs a digital marketing agency and lives in the Williamsburg section of Brooklyn, said she found out about the exhibition on social media. She described herself as “a massive Hov fan” who has a “Vol. 3 … Life and Times of S. Carter” rug in her apartment.

The Jay-Z card she picked up a few days later is the first physical library card she has owned. “Seeing a rapper be on something as mainstream and as massive as a library card, it’s just phenomenal,” she said.

Dr. Barracks felt similarly. While waiting in a 20-minute line for his card, he said he had heard fans “bro-ing out” about which album was superior.

“We don’t always see Black stories like Jay-Z’s take over everyday public spaces,” said Dr. Barracks, whose research centers on Black joy. “Every time people go to get other books, maybe it’ll encourage them to remember that our stories exist in the library, too.”