McCaw has a sore neck and leg after a rugged 80 minutes on Saturday night, when his side beat the Springboks 21-11 to secure half a hand on the Rugby Championship trophy.
All Black coach Steve Hansen said McCaw was probably feeling the sorest of the players after a tough test at Forsyth Barr Stadium.
"I have instructed them to get away from rugby, enjoy their family and children for those who have them. Then we'll get back on the circus come next Saturday."
Injured first five-eighth Dan Carter is not yet up to running at full pace as he comes back from a injured calf.
Hansen said Carter was expected to be available for the trip, though that call would not be made until later in the week.
An option was to take Beauden Barrett as a back-up for Carter, even if he was cleared fit, and leave a prop or loose forward behind.
McCaw suffered a blow to the neck late in the game when he grabbed a ball which had bounced off an upright.
Earlier, the All Black skipper had been hit by a flying elbow from Springbok replacement prop Dean Greyling, which sent the Springbok to the sideline for 10 minutes.
Hansen labelled the hit a cheap shot.
"The judiciary will do what they have to do and it is out of our hands. It was a cheap shot and that is the end of it for us."
Greyling was last night given a two-week ban by Sanzar duty judicial officer Paul Tully, who accepted a guilty plea from the player but felt that, although there was no injury caused, the action had the potential to cause serious injury. Greyling will be out of action up to and including September 30.
The All Blacks will fly out to Buenos Aires on Saturday to prepare for the test against Argentina on September 30 (NZ time).
After that game, they will journey to South Africa to take on the Springboks in Soweto, in front of 90,000 fans on October 7.
It makes for a lengthy couple of weeks for the men in black but the next few days of rest will be time well spent after a bruising battle on Saturday night.
Hansen got exactly what he expected from the South Africans.
"It was not a complete performance, obviously, but it was a torrid test match. They were desperate, playing with a lot of commitment and physicality.
"Sometimes it tests your character and I was really, really pleased with the character of our elder statesmen and our younger players.
"For some of them it was the first time in that arena and that sort of rugby, and I thought they came through well."
Hansen said the side had no complaints about the surface and the venue on what was a top night.
"You could not ask for a better place to play. It is pretty special."
