The star's second studio album Pink Friday: Roman Reloaded was eligible to be nominated for prizes at the ceremony, but did not appear in a single category.
"Congrats to @LilTunechi and @Drake and @Hit_Boy on their Grammy Noms butttt…..," Bryant tweeted, before adding: "They was on some bulls**t for not nominating @NICKIMINAJ."
Minaj has been nominated for four Grammy Awards over the past two years, including nods for 'Best New Artist' and 'Best Rap Album'. However, she has yet to win a prize at the ceremony.
Meanwhile, Justin Bieber's manager Scooter Braun was angry the singer hadn't received any nominations, while fans also protested the absence of One Direction.
Watch the music video for Nicki Minaj's new single 'Freedom' below: