Hield was given a flagrant foul 2, which results in an automatic ejection.
The incident took place in the second quarter while Hield was fighting around a screen.
After the game, Hield said there was nothing intentional about his hit on Cousins and noted that if Cousins had thought it was intentional, he likely would've gone after Hield.
"Nothing was intentional. DeMarcus sold it," Hield said. "Then on slow-motion [replay], it looks worse than it is."
The incident came after Cousins received a technical foul of his own -- his league-leading 17th of the season. Cousins picked up his tech for hitting Pelicans big man Donatas Motiejunas in the face while fighting for a rebound in the first quarter.
Cousins has already been suspended once for reaching the 16-technical-foul plateau. An 18th technical foul would trigger another automatic suspension.
"I can't be myself," Cousins said. "Me playing the way I play is what makes me the player I am. I'm trying to find a way to do what these guys are asking me to do. Obviously what I've been doing is not acceptable. It's not easy, but I'm trying to find a way."
Information from The Associated Press was used in this report.