Red Bull Racing team officials said Vickers, 26, was hospitalized for tests Wednesday night. The team replaced Vickers with Casey Mears in the No. 83 Toyota for the race at Dover International Speedway.
"Our main concern right now is with Brian and his health and recovery," Red Bull Racing General Manager Jay Frye said in a statement. "All things are looking good at the moment. This is just a minor setback. We appreciate Casey filling in this weekend and know he will represent the team well."
Vickers is 20th this year in Sprint Cup points after a 10th-place finish last Saturday. Last year he qualified for the Chase for the Cup for the first time since joining the circuit in 2004.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys