The 24-year-old is set to miss up to two months of action after it was confirmed he would need surgery after diving for a ball in domestic cricket this week.
"He landed heavily on his thumb while fielding, with scans indicating the ligament has fully ruptured and retracted," said New Zealand physio Paul Close in a statement on blackcaps.co.nz. "After consultation with NZC medical staff and a hand specialist, it was decided the best course of action is for him to have surgery."
Close continued: "He will commence rehabilitation immediately following the procedure, with a view to him returning to cricket during the home summer.
"The procedure is likely to keep him out of the game for six to eight weeks."
The news is a major blow to the Black Caps' hopes ahead of the two-Test series, which begins in Cape Town on January 2.
Southee played a key role as New Zealand drew their recent Test series in Sri Lanka 1-1. The right-armer grabbed 12 wickets at an average of 13.8.
New Zealand are yet to name a replacement player, with a three-match one-day international series also to follow.