McCaw will take the field for the first time in Super rugby this season after surgery for a stress fracture of his right foot, but Carter has tweaked the same right hamstring he injured against the Sharks at Twickenham two weeks ago, an injury which ruled him out of the 27-0 win against the Bulls in Timaru on Saturday.
He was earlier today named in the starting XV but felt his hamstring tighten halfway through training this morning and immediately left the field.
He will be reassessed early next week as to his availability for the Crusaders' next match, against the Highlanders in Nelson on April 23.
Matt Berquist, who wore the No 10 jersey against the Bulls, will start at first five-eighth against the Chiefs while Tom Marshall comes on to the bench.
Meanwhile, Owen Franks starts at tighthead prop, with his brother Ben moving to loosehead, and Wyatt Crockett dropping to the reserves bench.
Kahn Fotuali'i has earned his first start of the season, replacing Andy Ellis at halfback.
Crusaders coach Todd Blackadder is expecting a big challenge from the Chiefs.
"These derby matches are especially important in this season's competition due to the conference format. Traditionally they always carry extra spice and it will be a tough, physical match up there," he said.