CCTV footage showed Warner apparently turning on De Kock as the players walked up a narrow staircase leading to the dressing rooms during the tea break on Sunday.
Vice-captain Warner had to be restrained by his team-mates as he appeared to lose his temper, reportedly over a jibe about his wife Candice, although the South Africans blamed him for sparking the argument.
The incident is in the hands of match referee Jeff Crowe.
"The incident was discussed between the two team managers and the match referee last night and it is now in the hands of the on-field umpires and the match referee," Cricket Australia said on Tuesday.
"Both teams were reminded by the match referee of the spirit in which the game should be played."
The controversy has divided opinion, with Warne calling on the players to avoid "personal" comments -- while also urging them to "have a beer together" and patch things up.
"Chat, banter, sledging has always been a part of any series between SA & Oz. Both sides always give it out," he tweeted.
"Respect is the key & and I hope nothing personal was said to any player towards anyone from either side. Have a beer together afterwards & get on with it - stop the whinging!"
Former England captain Michael Vaughan suggested Warner had a reputation as a sledger and it was only a matter of time before insults were hurled back.
"Correct Warney....but it's clear plenty of personal nonsense has been spoken & the man in question I hear from many has been doing it for a while so I guess someone eventually was going to touch a nerve with a response," he said on Twitter.
South African manager Mohammed Moosajee also blamed Warner.
"There were words said out on the field. If you are saying something you've got to take it and that's the opinion of Quinton," he said.
Australian great Adam Gilchrist also took to Twitter to voice an opinion, calling the spat "ugly".
"Can only assume something very personal has been thrown at @davidwarner31 for this type of reaction. Not a good look all round," he said.
Former South African skipper Graeme Smith agreed it was not good for cricket, but suggested Warner only had himself to blame in an online reply to Gilchrist.
"Gilly - Warner crossed many personal boundaries with the South Africans, so we can't be surprised when there is eventually a reaction," he said.
"If players are happy to give it, they have to be prepared to take it, too. On both sides! But agreed not a good look."
First Published: March 6, 2018, 11:36 AM IST