Curry made the allegation to referee Ben O’Keeffe just after the 20-minute mark of the hard-fought semi-final, with the exchange picked up by the ref mic.
“Sir, if their hooker calls me a white c***, what do I do?” Curry inquired of O’Keeffe.
“Nothing, please,” responded the official, before adding a few moments later, “I’ll be on it,” in what may have been an unrelated comment.
The alleged incident itself could not be heard on the television broadcast.
The South Africa hooker subsequently appeared to refuse to slap away Curry’s attempted handshake at full time.
A statement from South Africa Rugby said: “We are aware of the allegation, which we take very seriously, and are reviewing the available evidence.
“We will engage with Bongi if anything is found to substantiate the claim.”
Mbonambi is among the defending champions’ group of senior leaders and finished the game as captain after Siya Kolisi’s substitution.
Curry refused to comment on what was said post-match, though did confirm that he felt Mbonambi’s remark had crossed the line.
Both teams are able to refer any incident of concern to the match citing commissioner within 24 hours of the final whistle. The citing officer then has 12 hours to determine if they will lay in charges.
World Rugby refused to comment while this 36-hour window was open.
Deon Davids, South Africa’s forwards coach, stressed afterwards that he was “not aware” of anything that was said. “If it was discussed, I’m not sure what the comment was or when it was said. I don’t know.”