Warner was charged with bringing the game into disrepute and fined 75 percent of his match fee from the first test for an ugly verbal confrontation with South African wicketkeeper De Kock.
De Kock was fined 25 percent of his match fee for the heated off-field exchange.
The ICC stopped just short of banning Warner for the match that starts in Port Elizabeth on Friday.
The vice-captain was handed three demerit points by the ICC, Cricket Australia said on Wednesday.
Should a player receive four or more demerit points within a two-year period, these are converted into suspension points. A suspension point amounts to a ban from one test or two ODIs, or two T20s, whichever come first.
The incident between Warner and De Kock has sparked a war of words between the two camps, with each blaming the other for overstepping the boundaries of what is acceptable.
CCTV footage from the players' tunnel on day four of the first test in Durban showed Warner and De Kock involved in a fiery exchange as players climbed the stairwell to their dressing rooms during the tea break.
Warner had to be restrained by team mates during the fracas.
Another video from just before the incident surfaced on Wednesday showing Warner repeatedly calling De Kock a "sook", which is Australian slang for somebody that is perceived to be soft.
De Kock also had one demerit point added to his record by the ICC.
Warner was not the only Australia player punished by the ICC following their tempestuous 118-run victory in Durban.
Spinner Nathan Lyon was fined 15 percent of his match fee for breaching the ICC's code of conduct as he intentionally dropped the ball onto a sprawled AB de Villiers after the South African batsman had been run-out in his country's second innings.
(Reporting by Nick Said; Editing by Christian Radnedge and Toby Davis)
