This week, Australian all-rounder Mitchell Marsh was also ruled out of the opening Pakistan Test after injuring his hand punching a wall, with coach Justin Langer branding him "an idiot".
With an outclassed South Africa two-nil down in the series in India, Markram called his actions "unacceptable" and said that "to let the team down is what hurts me the most".
"We understand in sport that emotions run high and sometimes the frustration gets the better of you as it did for me, but like I said, it's no excuse," he said in a statement.
The incident happened after Markram was out for his second duck of the second Test in Pune last Sunday as India won the match by an innings and 137 runs, and with it the series.
He was out second ball in both innings and failed to review an lbw decision in the second, although replays showed the ball would have missed his stumps.
No replacement has been called up for the match starting in Ranchi on Saturday, opening the way for Zubayr Hamza to make his second Test appearance.
But South Africa, who weren't helped by losing two tosses on batting-friendly Indian wickets, will have to decide on a makeshift opening batsman, with no other specialist in the touring party.
No time frame was specified for Markram's absence. According to the CSA statement, Markram has already left India and will see a specialist in South Africa.