The Aussie opener has been slapped with a grade two contrary conduct charge which might see him rubbed out of the second Test, while de Kock was hit with a grade one charge for the altercation.
"Australia vice-captain David Warner and South Africa's Quinton de Kock have been reported for breaching the ICC code of conduct", cricket's governing body said in a statement.
Australia and South Africa have until Thursday morning AEDT to officially respond to the reports, with both having the option to appeal.
Match referee Jeff Crowe has had to sift through claim and counter-claim regarding the incident that occurred at tea on day four of the game.
Earlier on Tuesday, Australian coach Darren Lehmann said that he was "certainly supporting" Warner, and that his position as the vice-captain was not in jeopardy.
After Australia's 118-run win on Monday, the visitors' captain Steve Smith pointed towards De Kock as the instigator.
Panellist and veteran News Corp cricket writer Robert Craddock said the footage needed to be shown, as it showed Warner's true nature on the cricket field. "Both sides always give it out".
Australia maintain that Warner was provoked by personal comments that de Kock made about his wife, but the opening batsman has accepted the charges of bringing the game into disrepute and is now one demerit point away from a ban. "We've got to make sure we don't cross the line", he said.
Taking on to twitter, Warne wrote, "Chat, banter, sledging has always been a part of any series between SA & Oz".
Smith said after the game he is not aware of the Australian team crossing the line with any personal sledges during the spiteful fourth day.
The second Test if the four-match series, which Australia lead 1-0, begins in Port Elizabeth on Friday.
"Australian teams have generally been at the top of the pile, not every minute of those times, but generally they're a very competitive, world-class team, and some would say they don't need to do that".
South African manager Mohammed Moosajee also blamed Warner. I'm not 100 per cent sure but as far as I'm aware I don't think we got personal. "It's unnecessary to take it to places that it sometimes went", cricket.com.au quoted Smith as saying.
"I don't know how their team manager can hear from where he's sitting".
"Gilly - Warner crossed many personal boundaries with the South Africans, so we can't be surprised when there is eventually a reaction", he said.