Philander pulled up after bowling just five overs for domestic side Cape Cobras on Thursday and is set to take no further part in the match at Newlands.
South Africa team manager Dr Mohammed Moosajee said preliminary scans revealed a Grade One tear that could keep the right-armer out for two weeks.
The first of the two-Test series against the Black Caps is in Cape Town on January 2, leaving Philander in some doubt to take his place.
"MRI scans revealed that Vernon suffered a Grade One strain to his left hamstring. Injuries of this type usually have a 10 to 14 day recovery period," Moosajee said in a statement.
"We will assess the injury as the week progresses, and this will help determine whether his availability for the Test series will be affected.
"At this point he will not bowl again during the match and will only bat if necessary."
Philander missed the second Test of the recent 1-0 series win in Australia after complaining of back soreness on the eve of the match.
- Sports & Recreation
- Cape Cobras