Hendrick Motorsports said Earnhardt will sit out races in Charlotte and Kansas, and Regan Smith will replace him in the No. 88 Chevrolet.
Earnhardt, who celebrated his 38th birthday on Wednesday, was injured in a 25-car, last-lap accident Sunday at Talladega. Because he was able to drive his car away from the accident teammate Jimmie Johnson even caught a lift on the window back to the garage Earnhardt was not required to go to the care center for an examination at the time.
Immediately after the race, he called restrictor-plate racing "bloodthirsty" and said he no longer had any desire to compete at Daytona and Talladega.
The wreck was at least the second hard hit Earnhardt has had this season. He struck the wall extremely hard during the Goodyear test at Kansas when his right front tire failed, an accident driver Brad Keselowski tweeted about moments afterward.
Earnhardt, who attended a Washington Redskins exhibition game later that evening, was asked Thursday why didn't he seek attention after the Kansas accident.
"Too stubborn," he said. "With the Chase coming up, if I was to volunteer myself for medical attention, I didn't know how difficult it would be to get back in."
He added: "I knew something was not right. But I decided to just push through. I'd had concussions before."
Earnhardt earlier this season snapped a 143-race winless streak dating to 2008.