CCTV footage from the tunnel at Kingsmead showed Australia vice-captain Warner and De Kock involved in a fiery discussion as players climbed the stairwell to their dressing rooms during the tea break on day four.
The footage revealed Warner being restrained by his team-mates before his captain Steve Smith ushered the opening batsman away.
"It's rather unfortunate that the incident took place and certainly not in the spirit of the game," South Africa's team manager Mohammed Moosajee said. "The match referee had spoken to us after the day's play. We will await any further communication from the ICC around this incident."
Cricket Australia (CA) said it was also looking into the incident.
"CA is aware of reports of an incident between players in Durban," a spokesperson for the Australian governing body said.
"CA is working to establish the facts of what has occurred and will not be commenting further until that has been done."
Meanwhile, Lyon has been fined 15 per cent of his match fee and had one demerit point added to his record for dropping the ball on to De Villiers as the South African batsman was on the ground after being run out by Warner on Sunday.
Match referee Jeff Crowe reviewed the incident and adjudged that the action was contrary to the spirit of cricket, a level one offence, and Lyon, who is believed to have apologised to De Villiers, has accepted the charge.