Bowe was arrested on speeding and controlled substance charges last weekend and faces a court date next month.
Chiefs coach Andy Reid told reporters on Wednesday: "It is a legal matter and that's the way we'll handle it. Let it run its course there. Dwayne will play, he'll start."
The 29-year-old has 33 catches for 369 yards so far this season, recording two touchdowns.
The Chiefs top the AFC West from the Broncos, with an unbeaten 9-0 record.