South Africa's Mbonambi accused of racial slur aimed at England's Curry
Mbonambi is the Springboks' only specialist hooker due to Malcolm Marx's tournament-ending injury, although converted back row forward Deon Fourie has covered from the bench.
Mbonambi is alleged to have addressed England backrow forward Curry with "you white (followed by an expletive)".
Curry approached referee Ben O'Keeffe about half an hour into Saturday's hard-fought match in Paris to report the alleged comment and asked what he should do in response.
"Nothing, please," replied O'Keeffe.
Curry was asked after South Africa had edged England 16-15 to reach the final whether Mbonambi, who also appeared to refuse to shake the England player's hand at the end of the match, had said something he had taken issue with.
"Yeah," replied Curry, before adding that "it does not need to be talked about".
South Africa Rugby said on Sunday they would look into the matter.
"We are aware of the allegation, which we take very seriously, and are reviewing the available evidence," it said.
"We will engage with Bongi if anything is found to substantiate the claim."
Verbal abuse in rugby is rarely penalised, although England prop Joe Marler and South African Jacques Potgieter have been punished in the past.
Marler received a two-match ban for remarks addressed to Wales' Samson Lee in 2016 and Potgieter was fined for an on-field homophobic slur in a Super Rugby game in 2015.
The Springboks, though, will be nervously awaiting the citing deadline which falls on Monday morning.
They can ill afford to be without Mbonambi, who was man of the match in the quarter-final win over hosts France, for next Saturday's final with fellow three-time champions New Zealand.