The 34-year-old flanker was briefly knocked unconscious after being hit by a knee to the temple during last week's match against the Auckland Blues.
After McCaw came to training still suffering a mild headache on Monday, the team decided not to risk him, coach Todd Blackadder said.
"He was a little bit blurry and felt a little bit off, so it's best not to risk him," Blackadder told reporters in New Zealand on Tuesday.
"He just got his head on the wrong side and just got kneed in the temple. Even after the game he was really chipper and was fine, and even today, he was 100 percent, but it's just not worth risking him. All signs are pretty positive. Hopefully, he's back for next week."
Matt Todd is likely to step in as the starting number seven against the table-topping Hurricanes in Wellington but the loss of the New Zealand skipper will be a big blow to the Crusaders (5-5), whose hopes of making the playoffs are on a knife-edge.
All Blacks fullback Israel Dagg will also miss another match for the Crusaders as he battles to recover from a calf injury.

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