"Eben's father has passed," a team spokesperson told Reuters.
With regular skipper Siya Kolisi sidelined with a knee injury, Etzebeth was set to play for the world champion Springboks for the first time this season after recovering from injury.
However, South African media reports citing team sources said he would be given time to decide whether he would play against the All Blacks in Auckland on Saturday.
The team declined to confirm his place in the matchday squad.
Coach Jacques Nienaber had welcomed the prospect of Etzebeth returning.
“Eben has been working very hard in the last few months to make a full recovery from his shoulder injury and it’s great to see him return to the field in this important fixture," he said this week after naming Etzebeth in his squad.
South Africa opened their Rugby Championship campaign with a 43-12 win over Australia in Pretoria last weekend.