Stewart has not raced since he was driving a sprint car that struck and killed 20-eyar-old Kevin Ward Jr. at a dirt track in New York earlier this month.
Burton subbed for Stewart last week at Michigan and finished 37th in just his third Sprint Cup race of the season. Stewart was replaced two weeks ago at Watkins Glen by Regan Smith, who also came in 37th.
Stewart-Haas Racing has not announced when Stewart will return to the series, saying it's Stewart's decision. He has stayed out of the public eye since the Aug. 8 incident in Canandaigua, N.Y., when his car hit Ward, who had walked up the track after a crash and gestured toward Stewart.
An investigation into Ward's death is continuing.
Stewart also canceled an appearance at Plymouth (Ind.) Speedway scheduled for this weekend.
In 542 career Sprint Cup starts, Stewart has 48 victories, including one at Bristol in 2001.