Footage from a CCTV camera inside the player's grandstand shows Warner being hauled away by team-mates, including captain Steven Smith, as he screams abuse at De Kock while the teams walk up the steps during the tea interval on the fourth day.
In a statement issued by Cricket South Africa on Monday, team manager Mohammed Moosajee said: "It's rather unfortunate that the incident took place and certainly not in the spirit of the game".
The incident is in the hands of match referee Jeff Crowe, with no immediate clarity about when a decision could be expected.
Cricket South Africa also condemened the incident and said it will wait upon further communication from the ICC over the incident.
A furious Warner had to be restrained by three of his teammates - Usman Khawaja, Tim Paine and eventually Smith - as several media reports claimed that de Kock made comments on Warner's wife Candice.
Cricket South Africa and Cricket Australia said they were both were aware of the incident and awaiting more details.
Du Plessis reiterated that he expects to receive verbal comments from Australia when he is batting, and went so far as to say that he would be "disappointed" if it didn't happen. De Kock reviewed the verdict but it only delayed the inevitable. Meanwhile, personal insults were at the root of a row between Warner and de Kock, their captains said.
"In any sporting contest, in any contest, when you start getting a bit violent on or off the field it's a no-brainer, it's not acceptable".
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The less interest you take in Warner the better. "There was a real difference in skill with the reverse swing", said Du Plessis, who said Starc and South Africa's Kagiso Rabada were the two stand-outs.
Relations between the Australian and South African teams have become incredibly strained once again.
Warner gave a frenzied serve to Aiden Markram and AB de Villiers, having run the latter out for a duck during the morning session on day four.
Warner's behaviour came under the spotlight earlier on the fourth day when he ran out AB de Villiers after a mix-up with Markram with him then yelling in Markram's direction during the celebration.
For his part the South African wicket-keeper De Kock takes it all in his stride - not allowing Warner's tirade to unsettle him. "We're aggressive. we're hunting as a pack". "Because the two players in question, they might have had a heated exchange out in the middle, heated exchange in the aisle as they were going into the change rooms and then they might have had a beer at the end of the game and it's all sorted itself out".
The tourists asked, prior to the start of the four-Test series, for stump microphones to be turned down between balls.
"Quinton said there was personal stuff that was but he was initially the victim and when he had a go at David‚ David was aggressive towards him".