Brad Haddin will replace Gilchrist with Australia needing to win or tie to regain the Chappell-Hadlee Trophy.
"It's important his workload is managed with four Tests and a one-day series ahead," said chairman of selectors Andrew Hilditch.
Coach Tim Nielsen denied that rotating players is a sign of arrogance.
"It was planned a month ago when we looked at the programme," he said.
"It gives us a chance for him to go home to Perth for a bit of a break and come back to Melbourne [to play India on Boxing Day] fresh, which was always important for us heading into the first Test."