Etzebeth lost his father Harry to cancer on Tuesday, after the lock had been selected to lead the side for Saturday's clash with the All Blacks.
The 31-year-old has chosen to line-up in what could be the Rugby Championship decider in a shortened competition this year to accommodate the Rugby World Cup in France.
"Eben's loss, which is also our loss because we are a family, is very sad. We are with him," the Springboks' assistant coach Mzwandile Stick told reporters on Friday.
"If there is one thing about us as a team, we are there for each other.
"Eben has made the choice to play. I would like to think he is doing it for his dad but it is a big loss for us as a team to lose a parent."
The Boks have not tasted victory in Auckland since 1937 but South Africa have won two of their last three matches against the All Blacks, and claimed a win and a draw in their previous two visits to New Zealand, with both matches staged in Wellington.
"We have spoken about playing the All Blacks away from home and how special it is to win," Stick said.
"The majority of us were there in 2018 when we won in Wellington. We all live for that, to come to New Zealand and play the All Blacks."
South Africa swept aside Australia 43-12 in Pretoria last weekend but have made 10 changes for the match in Auckland.
One of those to keep their place is hooker Bongi Mbonambi.
"It is a different challenge," Mbonambi said.
"Australia was a good start but we have quickly put it behind us. We have put all our focus into this week.
"Both teams will want to make a statement before the World Cup."
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