He got through the endurance classic in Peru then underwent surgery last month on the wrist, which his doctor said was "collapsing into the wrong position".
It has scuppered plans for Price to continue his role with the Mitsubishi-backed Team Triton at the Superloop Adelaide 500.
Price's SuperUtes foray began last year at the series opener in Adelaide, followed by a second outing at Winton before his two-wheel commitments took over.
A 2019 program for Price was set to feature at least four of the eight rounds, including Adelaide, but that is now on hold until later in the year.
"It's no secret he had desire to come back and be a big part of our team, he is probably one of the inspirations and big reason why we put the team together," team manager Craig Dontas told Supercars.com.
"We sat down and worked out what the best plan was, building it around his international schedule, it was always dependent on how he pulled up after Dakar.
"He was scheduled to be testing early February, but with his injury, obviously he is out of action, he is going to take a lengthy time to recover from the surgery.
"There is just no risking where it is at, they said probably a four-month recovery, so he is not in the car.
"It hurts Adelaide, but it still puts us in good position for the back half of the year, so events like Townsville, Gold Coast and Newcastle, with the potential of Bathurst as well.
"You will probably see him back in for three of the marque events later in the year, pending his international schedule."
Barbour grabbed two wins from six starts, including Sandown round honours, in 2018
Dontas will step into the #87 Mitsubishi in Adelaide, as part of an expanded three-Triton effort.
The squad had a rotating driver roster in 2018, but will field Elliot Barbour and Cameron Crick full-time this year.
"Elliot's sole focus is to concentrate on driving and winning," Dontas added.
"Then with Cam, I see his work ethic and hunger to get in and really improve.
"If you want a young and up-comer who is going to give you 110 percent, Cam was the guy.
"He's a likeable guy that is going to give you 110 percent on and off the track, which is always a good thing.
"I put the decision across to Mitsubishi and they said this is what they want to do; put their focus around Elliot as the lead guy, have Toby at the front as well and then having another young up-and-comer who we can build a future with.
"It gives us an opportunity to put our best foot forward towards winning that championship and we're not going to stop until we've done it."
The eight-round 2019 ECB SuperUtes Series starts on February 28-March 3, as part of the Superloop Adelaide 500.