Velez was sent home on the singing competition Thursday after he sang the Perry Como hit "It's Impossible." Minaj slammed his Wednesday performance of The Four Tops' "I Can't Help Myself (Sugar Pie, Honey Bunch)" with fellow contestants Lazaro Arbos and Burnell Taylor.
"I'm gonna act like I didn't see that or hear it," she said, before ordering the trio to leave the stage, The Hollywood Reporter said.
In an interview after he was ousted from the show, Velez said he agreed with Minaj's critique that the performance was weak, but questioned her professionalism.
"When she went crazy -- when she was like 'get off the stage, blah blah blah' and it's just like 'whoa Miss Minaj, I need you to calm down please,' " he said.
The judges have a collective one-time-only save option but did not choose to exercise it to keep Velez on the show.
Following Velez's complaints, Minaj took to Twitter, saying the female contestants on the show are too good to use the save on a male contestant.
"If Curtis [Finch Jr.] didn't get SAVED, NONE of u get saved. Best male voice of the SEASON!!!!!!!!!!! #TruthTea," Minaj tweeted.
"Trust me BEW BEW. If EYE didn't want u in that TOP, YOU wldnt have been in that TOP. Fought for ALL of You. So just simply b gracious," she added.