Philander took two wickets for 17 runs in 12 overs in between bouts of what was said to be stomach illness on Thursday's rain-marred first day.
But he only bowled five more overs in Friday's first session before leaving the field and has yet to return to play.
A team spokeswoman said Philander had been taken to hospital for tests to determine the precise nature of his condition, which now appears to be more serious than initially thought.
He has also become an increasingly effective batsman, with Philander named man-of-the-match for his all-round contribution to South Africa's 340-run win in the second Test at Trent Bridge that saw the Proteas level this four-match series at 1-1.