New Zealand bowling spearhead Southee has a torn hamstring while de Kock is nursing a ligament injury to the index finger on his right hand.
Southee's injury left New Zealand sweating on the fitness of his new-ball partner Trent Boult who missed the second Test, won by South Africa by eight wickets, because of leg soreness.
Boult is in the squad for the third Test and has bowled lightly in the nets this week, but has yet to pass a final fitness test, although a team spokesman said there would be no replacement called up for Southee.
"While only a minor tear, he will not be fit for the upcoming match beginning Saturday," he said.
South African team management said a decision would be made Friday on whether influential wicketkeeper-batsman de Kock would play.
He injured the finger on the final day of the second Test.
Initial x-rays ruled out a fracture but continued discomfort has revealed ligament damage which could require several weeks rest.
If de Kock is ruled out, Heinrich Klaasen is expected to be his replacement in what will be his debut Test.
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