The cover depicts Elden as a four-month-old in a swimming pool, grasping for a dollar bill that's being dangled in front of him on a fishing line.
Now 30, Elden says his parents never signed a release authorising the use of his image on the album.
He also alleges the nude image constitutes child pornography.
"The images exposed Spencer's intimate body part and lasciviously displayed Spencer's genitals from the time he was an infant to the present day," legal papers filed in California claim.
Non-sexualised photos of infants are generally not considered child pornography under US law.
However, Elden's lawyer, Robert Y. Lewis, argues that the inclusion of the dollar bill (which was superimposed after the photograph was taken) makes the minor seem "like a sex worker".
The legal case also alleges that Nirvana had promised to cover Elden's genitals with a sticker, but the agreement was not upheld.
Elden alleges his "true identity and legal name are forever tied to the commercial sexual exploitation he experienced as a minor which has been distributed and sold worldwide from the time he was a baby to the present day".
He claims he "has suffered and will continue to suffer lifelong damages" as a result of the artwork, including "extreme and permanent emotional distress" as well as "interference with his normal development and educational progress" and "medical and psychological treatment".
He is asking for damages of at least $150,000 (£109,000) from each of the 15 defendants, who include surviving band members Dave Grohl and Krist Novoselic; the manager's of Kurt Cobain's estate; Cobain's former wife Courtney Love; and photographer Kirk Weddle.
Representatives for Nirvana and their record labels have yet to respond to the claims.
Elden has recreated the album cover several times as a teenager and adult - always wearing swimming trunks - to mark Nevermind's 10th, 20th and 25th anniversaries.
However, he has sometimes expressed ambivalence about the photoshoot. In 2016, he told Time Magazine that he "got a little upset" about his notoriety as he grew older.
"I just woke up already being a part of this huge project," he said. "It's pretty difficult - you feel like you're famous for nothing.
"It's hard not to get upset when you hear how much money was involved," he continued. "[When] I go to a baseball game and think about it: 'Man, everybody at this baseball game has probably seen my little baby penis,' I feel like I got part of my human rights revoked."
In other interviews, he has been more upbeat about the image.
"It's always been a positive thing and opened doors for me," he told the Guardian six years ago. "I'm 23 now and an artist, and this story gave me an opportunity to work with Shepard Fairey for five years, which was an awesome experience. He is a huge music connoisseur: when he heard I was the Nirvana baby, he thought that was really cool."
In 2008, Spencer's father Rick recounted the photo shoot to US radio network NPR, saying he had been offered $200 to take part by Weddle, who was a family friend.
"We just had a big party at the pool, and no one had any idea what was going on!"
The family quickly forgot the photoshoot until, three months later, they saw the Nervmind album cover blown up on the wall of Tower Records in Los Angeles.
Two months after that, NPR's article said, "Geffen Records sent 1-year-old Spencer Elden a platinum album and a teddy bear".
The album, which included the hits Smells Like Teen Spirit, Come As You Are and Lithium, went on to sell 30 million copies around the world.
-bbc
İhbar Hattı
