The 2020 champion suffered an injury to his left leg while snowboarding in Colorado, a Hendrick team statement said.
He was scheduled to undergo surgery on Friday night, and his length of recovery is currently unknown.
Elliott will be replaced by Xfinity Series regular Josh Berry, the 32-year-old a five-time race winner at the second tier of NASCAR competition.
He has only made two previous Cup Series starts, with best finish coming at Michigan with Spire Motorsports in 2021 when he finished 26th.
Berry finished fourth in the Xfinity standings last year with JR Motorsports, the team owned by Dale Earnhardt Jr.
“Chase’s health is our primary concern,” said Rick Hendrick, owner of Hendrick Motorsports.
“He’s spoken with several members of our team and is understandably disappointed to miss time in the car.
“Of course, he has our full support, and we’ll provide any resources he needs. We hope to share another update later this weekend.”
Sunday’s race will be the first Elliott has missed since becoming a fulltime driver in the Cup Series in 2016. In 259 career starts, he has 18 wins.
He finished second to Kyle Busch in last weekend’s Fontana race after an early exit from the Daytona 500.
But missing races won’t necessarily derail Elliott’s 2023 title chances – Busch himself suffered a broken leg and foot at Daytona in 2015 but progressed to the playoffs on race wins and secured his first Cup title.