Minutes before the tea break, Elgar tried to duck a short delivery from Yadav, who was in the middle of a hostile spell of short-pitched bowling.
Elgar was hit just above the ear and immediately fell on the ground, calling for medical help. He was batting on 16 off 29 balls when Umesh bouncer struck him.
Elgar can return to competitive action only after six days said the Cricket South Africa (CSA).
"The opening batsman will be closely monitored over the next 24 hours, followed by reassessment every 24 hours until signs and symptoms resolve. The soonest he can return to play is in six days’ time in keeping with the standard concussion management protocol," CSA said in a statement.
Elgar is the third concussion substitute after Marnus Labuschagne of Australia (in place of Steve Smith during Ashes Test at Lord's) and Jermaine Blackwood (vs India replacing Darren Bravo).