Smith was named on Saturday to return to the captaincy after missing the third and final Test against Australia.
However, team physiotherapist Shane Jabaar today rated his chances of playing as only 50-50. The left-hander is still wearing a splint on the finger.
''Graeme consulted a hand specialist yesterday and we are trying to improve his finger that has been in a splint since the injury,'' Jabaar said in a statement today.
South Africa's first practice session of the week is scheduled for Thursday.
''He will bat in the nets on Thursday, and then we will have a better idea of his fitness to play in the first Test,'' Jabaar said.
The 25-year-old suffered ligament damage and severe bruising to the ring finger of his left hand during fielding practice on March 30, the day before the final Test against Australia.
If Smith is ruled out of the opening match of the three-Test series against New Zealand, Jacques Kallis will once more take over the captaincy.
Australia won the series in South Africa 3-0.