Chiefs general manager John Dorsey said on a Kansas City radio station Tuesday that he was aware of the incident but wouldn't comment further.
News of Bowe's arrest comes as the AFC West-leading Chiefs (9-0) are coming off their bye week and preparing to play the division rival Broncos (8-1) on Sunday night in Denver.
Bowe, who signed a five-year, $56 million contract with the Chiefs last offseason, is second on the team with 33 receptions and third with 369 receiving yards.
According to a statement released by police, Bowe was pulled over shortly before midnight on Saturday for doing 48 mph in a 35 mph zone. The officer detected the strong odor of marijuana coming from the car. After a subsequent search by a police K-9 dog, more than 10 grams of marijuana were found in two containers in Bowe's car.
The K-9 also found 4.2 grams of marijuana in a backpack in Bowe's car. A passenger, identified by police as George A. Thompson, told police the backpack belonged to him. Two hand-rolled cigarettes containing 2.2 grams of what police believe to be marijuana were found on Thompson, who was arrested for possession of a controlled substance.
A second passenger in the car was not arrested.
Bond was posted for Bowe at $750 and Thompson at $500. A Dec. 18 court date was set.
Bowe was suspended for four games in 2009 for violating the NFL's policy on performance-enhancing drugs. That program, however, is separate from the substance-abuse policy that governs use of illegal drugs and abuse of alcohol.
ESPN NFL Insider Ed Werder contributed to this report.