Benatia, who is on loan at Juventus from Bayern Munich, has not commented publicly on what happened during the television interview.
The broadcaster has since apologised and promised to find out who made the “unacceptable” comments.
“Rai is sincerely saddened by the deplorable episode of racism involving the Juventus player during the broadcast of Champagne Football,” it said on Sunday, adding that the insult had not been heard by the viewers.
Benatia has made 17 league and cup appearances for Juventus, who are closing in on a sixth successive Serie A title and are in the Champions League semi-finals.
Juventus released a statement, saying: “Following the regrettable insult Medhi Benatia heard through his earpiece during Calcio Champagne, Juventus Football Club wishes to express its concern over the incident.
“While acknowledging the Rai statement expressing solidarity, everyone – and the player first and foremost – deserves an explanation about what occurred.”
Meanwhile, Muntari was an unused substitute as relegated Pescara lost 1-0 at home to fellow strugglers Crotone on Sunday.
The former Portsmouth and Sunderland player was cleared to play after a one-match ban he received for protesting against racist abuse in last weekend’s match at Cagliari was overturned.
Muntari was initially booked for dissent, then received a second yellow card for leaving the field.
Before the ban was overturned, former Tottenham striker Garth Crooks called on players in Italy to strike in protest against Muntari’s punishment.