Rihanna, 24, was nominated in the top category - artist of the year - where she will compete with Bieber, Katy Perry, pop-rockers Maroon 5 and Canadian rapper Drake.
She also won nods for female soul/R&B artist and album for "Talk That Talk," and will battle Minaj, 29, in the female pop/rock artist category.
Minaj scored two nods for her album "Pink Friday: Roman Reloaded" in both the pop/rock and rap/hip hop categories this year, as well as a nomination for favorite rap artist, alongside Drake and American newcomer Tyga.
Minaj has been making headlines after joining the "American Idol" judging panel, where she was caught feuding on camera with fellow judge Mariah Carey in early audition rounds.
"Boyfriend" singer Bieber, 18, landed three nominations this year, tying with British boy band One Direction, Maroon 5, Drake and R&B star Usher.
Following in the footsteps of the Grammy Awards earlier this year, which hosted a tribute to electronic dance music, the American Music Awards introduced a new category in that genre, with David Guetta, Calvin Harris and Skrillex competing for the trophy.
Last year's big winners, Adele and Taylor Swift, who both scored three awards each, received one nomination each this year. Swift scored a nod for female country artist alongside Carrie Underwood and Miranda Lambert, while Adele was nominated in the favorite adult contemporary artist category alongside Kelly Clarkson and Train.
The closely-watched new artist category will be a battle between R&B singer J.Cole, indie-pop ban fun., Australian singer-songwriter Gotye, Canadian pop singer Carly Rae Jepson and One Direction.
The AMA winners are determined by fans through online voting, which starts on Tuesday.
The American Music Awards will be celebrating its 40th anniversary this year and the ceremony and performance show will be broadcast live from Los Angeles on Nov. 18.
Pop star and "The Voice" judge Christina Aguilera, who announced the nominees on Tuesday, was the first performer to be announced for the live show.
