The 28-year-old pace spearhead suffered a grade one tear of his left hamstring during the second test defeat in Wellington, New Zealand Cricket said.
"He felt discomfort following the second test in Wellington and as a precautionary measure was sent for a scan," read a statement.
"While only a minor tear, he will not be fit for the upcoming match beginning Saturday."
Kane Williamson's side are still sweating on the fitness of left arm seamer Trent Boult, who missed the eight-wicket loss at the Basin Reserve with pain in his hip/groin area.
Wicketkeeper BJ Watling told reporters on Wednesday that Boult was still not 100 percent and would be monitored by medical staff ahead of the match at Seddon Park in Hamilton, which starts on Saturday.
Southee will not be replaced in the squad with Neil Wagner and Matt Henry the remaining two pace options. All-rounders Jimmy Neesham and Colin de Grandhomme can also bowl brisk medium pace.
The hosts could still go into the match with two spinners. South Africa lead the series 1-0.
(Reporting by Greg Stutchbury; Editing by Nick Mulvenney)
