Renshaw was struck twice on the helmet, once while batting on day one and then again while fielding at short leg on day three, when he was taken from the field.
"Matthew Renshaw was struck on the helmet fielding close-in on Thursday afternoon and came off complaining of a headache," team doctor Peter Brukner said in a statement.
"He rested in the dressing room and then, when we returned to the hotel, we performed concussion tests and his cognitive, balance, co-ordination and reaction times were all within normal limits.
"However, on Friday morning he was still symptomatic and so we have taken the decision to withdraw him from the match as he is suffering from concussion.
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"We will continue to monitor him over the coming days and work with him to produce a gradual return to play."
Australia will have to bat with 10 men in their second innings as there is currently no provision for a concussion substitute in a test match.
Cricket Australia have experimented with replacements in non first class matches in the wake of the death of batsman Phillip Hughes, who was struck in the back of the head by a ball at the Sydney Cricket Ground in November 2014.
Brukner said the International Cricket Council (ICC), who decide the rules for first class matches, were likely to come under pressure to follow suit at the elite level as more and more cases like Renshaw's occur.
"The concern we have is without a concussion sub there is a lot of pressure on the player, the coach and the doctor to allow the player to continue," he told reporters.
"So it would be helpful in that regard if we had a sub that would make it easier to pull players out with a concussion. That’s for the ICC and the politicians to sort out really. I’m more concerned with looking after Matthew."
Bukner was quick to point out that he had come under no pressure from the Australia team management over Renshaw.
"I have to say the coach and the captain have been absolutely supportive," he said. "They’ve said to me all along ‘it’s your decision doc’. I’ve had no pressure at all to keep Matthew in the game."
Wicketkeeper Matt Wade, who missed much of Thursday's play with nausea, vomiting and diarrhoea, would be fine to play on Friday, Brukner said.
No play was possible in the first session of day four on Friday because of rain but was provisionally scheduled to get underway after the scheduled lunch break.
(Additional reporting by Greg Stutchbury in Wellington; Editing by Peter Rutherford)
