Stewart's decision was announced Wednesday and Jeff Burton will once again replace him in the No. 14 Chevrolet. Burton also drove Stewart's car at Michigan last week.
Stewart-Haas Racing is allowing Stewart to take the time he needs away from the track, and the three-time NASCAR champion is apparently taking it week-by-week.
Stewart has been in seclusion since the Aug. 8 incident at an upstate New York dirt track. He has not commented since he issued a statement the day after Ward's death.
Stewart also pulled out of the race at Watkins Glen, which began about 12 hours after his car hit Ward at event in Canandaigua, New York. Ward's car had spun into a wall as he and Stewart raced for position, and the 20-year-old climbed out to confront Stewart.
Authorities said the first car to pass Ward had to swerve to miss hitting the driver, who was gesturing toward the NASCAR star. The front of Stewart's car then appeared to clear Ward, but Ward was struck by the right rear tire and hurtled through the air.
Ward died of blunt force trauma, and authorities were still investigating the incident. Ontario County Sheriff Philip Povero has said investigators did not have any evidence to support criminal intent by Stewart, but the investigation is expected to last at least another week.
Stewart has 48 career Cup wins in 542 starts. He has one career win at Bristol, in 2001.
Burton made just his third start of the season last week. The 21-time Sprint Cup winner parted ways with Richard Childress Racing at the end of the season and is transitioning into an analyst for NBC. Burton won at Bristol in 2008 and has 15 top-10 finishes in 40 career starts.