The song, titled “Doom”, contained a reading of a Muslim text known as a Hadith, and caused uproar when it was played during the lingerie show.
The artist, who filed the suit anonymously, claims that they were bombarded with death threats after the incident.
According to TMZ, Rihanna contacted the artist about using the song for the show and was told to use a version of the song that did not include the sample.
However, the show’s producers allegedly played the wrong version.
The artist alleges that they have had to go into hiding since the incident and have been suffering from depression and anxiety as a result of the threats.
They are seeking $10m (£7.2m) in damages.
When the issue first came to light, the artist apologised online and said they were unaware the samples contained religious chanting.
Rihanna also apologised over the incident, issuing a statement that said: “I’d like to thank the Muslim community for pointing out a huge oversight that was unintentionally offensive in our Savage X Fenty show.”
“I would more importantly like to apologise to you for this honest yet careless mistake. We understand that we have hurt many of our Muslim brothers and sisters, and I’m incredibly disheartened by this!”
The Independent have contacted Rihanna’s representatives for comment.