The 'Super Bass' singer took to her official Twitter account to announce the news, mourning the loss of her relative.
Minaj wrote: "Lived in Brooklyn his whole life. My precious cousin. My baby. Killed last nite. My cousin Nicholas. Also goes by Juse… Murdered. Last nite. Near his home. Brooklyn, NY (sic)."
In addition, the musician's messages were accompanied by photos of her late cousin.
The news was met by an outpouring of sympathy from Minaj's friends and fans.
American Idol winner Jordin Sparks wrote: "Sending love & prayers to you and your family."
Showbiz blogger Perez Hilton added: "So horrible! Sending love and light and peace and strength to you and your family."
Cher Lloyd recently expressed her desire to work with Minaj, stating that she admires the rapper's ability to cause trouble.
Minaj is currently accompanying Britney Spears on her Femme Fatale tour.
Watch Britney Spears and Nicki Minaj perform 'Till The World Ends' at the Staples Centre in Los Angeles below: