Elliott, the 2020 Cup champion, suffered a fractured tibia in his left leg in a snowboarding accident in Colorado last week.
The team said in a statement on Tuesday that the 27-year-old is expected to be out for six weeks after successfully undergoing a three-hour surgery.
NASCAR Xfinity Series regular Josh Berry stood in for Elliott at Las Vegas Motor Speedway last weekend, finishing 29th.
Berry will continue to pilot the car on ovals for the foreseeable future, but Corvette Racing sportscar ace Taylor will step in for NASCAR's first road course round of the year at COTA on 26 March.
The 2015 GTE Pro Le Mans winner, 31-year-old Taylor claimed the 2017 IMSA SportsCar Championship's Prototype class and added GTLM division titles in 2020 and 2021.
He has also claimed two outright victories in the Daytona 24 Hours in 2017 and 2019, adding a GTLM class triumph in 2021.
Taylor is known to Hendrick as he has assisted the team in its preparations for running a modified NASCAR as a Garage 56 entry at Le Mans this year. It will be driven by Jenson Button, Jimmie Johnson and Mike Rockenfeller.
"We’re focused on getting Chase back to 100%, so we’ll take however much time is necessary and make sure he has the best resources available," said Rick Hendrick, owner of Hendrick Motorsports.
"Josh was impressive this weekend under difficult circumstances, and we look forward to having him drive the oval tracks until Chase is able to return.
"Jordan is a world-class road racer and has recently been working with our Garage 56 team preparing for the 24 Hours of Le Mans. He’ll be able to step in and do a great job at COTA."
Elliott started the year with a DNF in the Daytona 500, but quickly rebounded with a runner-up finish at Auto Club Speedway before his injury.
Hendrick president and general manager Jeff Andrews said at the weekend that Elliott had been in contact with his team.
"We all know Chase and he cares an awful lot about his race team and Mr. Hendrick," said Andrews.
"I think at the top of his mind, he's worried and concerned that he let Mr. Hendrick down and his race team down.
"I texted with him this morning, and he was asking how late his guys had to work and things like that with the swap-over. That's pretty typical Chase Elliott, but he's a great kid.
"He's got a huge heart and I can only imagine how hard it is. He's worried about how hard it is on us and we're worried about how hard it is on him."
