Otherwise, Reid said little about Bowe's recent arrest in nearby Riverside, Mo., on charges of possession of a controlled substance and speeding. Police said the controlled substance was marijuana.
"It's a legal matter," Reid said. "That's the way we'll handle it [and] let it run its course there."
Bowe, who signed a five-year, $56 million contract in the offseason and is second on the team with 33 catches and third with 369 receiving yards, issued an apology Wednesday for his arrest.
"I apologize to the Hunt family, Coach Reid, my teammates and Chiefs fans for the distraction I have caused the team this week. Due to the nature of the pending matter, I am unable to make any further comment on the situation," he said in a statement released by the team.
Bowe, who practiced with the Chiefs Wednesday, wasn't available to answer questions.
"Dwayne's been a team player since I've been here," Reid said. "He doesn't want to bring any problems."
If convicted, Bowe is subject to discipline from the NFL, according to the league's substance-abuse policy. The Chiefs are prohibited, under terms of the collective bargaining agreement, from disciplining Bowe before then, something Reid seemed to refer to Wednesday.
"Rules and regulations are put in place," he said. "We'll abide by the rules and regulations."
Bowe's attorney, Kevin Regan, also issued a statement.
"My investigation reveals that Dwayne Bowe is unequivocally, 100 percent innocent in this matter. We look forward to clearing his good name at our earliest opportunity," Regan said.
The arrest came as the 9-0 Chiefs are preparing for their biggest game of the season. Reid indicated he didn't believe the team, listed on many betting lines as big underdogs to the Broncos (8-1), would be distracted by Bowe's situation.
"I think this football team is focused in on the Denver Broncos,'' he said.
ESPN NFL Insider Ed Werder contributed to this report.