Reports indicate that Proteas wicketkeeper-batsman Quinton de Kock was called a "bush pig" by the Australians.
It was reported on Monday that personal insults were at the root of a row between De Kock and Australia's David Warner during the tea break of the fourth day of the first Test in Durban.
CCTV footage showed Warner apparently turning on De Kock as the players walked up a narrow staircase leading to the dressing rooms at the start of the interval at Kingsmead.
After Australia's 118-run win on Monday, the visitors' captain Steve Smith pointed towards De Kock as the instigator.
It is believed that De Kock made a derogatory remark about Warner’s wife.
"Those sorts of things are not on from both sides," Smith said at his post-match press conference.
"Getting personal on the field is not on. We were certainly very chirpy out in the field as well. As far as I'm aware, we didn't get personal towards Quinton.
"What he said got a little bit personal towards Davey and, as we saw, it certainly provoked an emotional response."
However, reports indicate that the Australians also got personal with De Kock.
Afrikaans website Netwerk24 said De Kock was labelled as a "bush pig" by the Australians, while The Guardian in England reported that it was Warner who called De Kock a “bush pig”.
Netwerk24 further reported that De Kock hit back after the Australians also made remarks about his mother and sister.
South African captain Faf du Plessis said the umpires needed to ensure proper behaviour on the field.
"From what I've heard there was a lot of personal stuff being said, to and from. Who started it, I don't know. If it was happening on the field it should have been nipped in the bud.
"The fact that it spilled over after the field shouldn’t have happened."