Bowe was pulled over shortly before midnight on Saturday for doing 48mph in a 35mph zone, according to a police report.
The officer then searched the car and found 10 grams of marijuana in two containers, as well as a further 4.2 grams in a backpack that belonged to a passenger, who was also arrested.
The pair will appear in court facing the charges on December 18.
Bowe is currently the Chiefs' second most prolific receiver with 33 catches this season, while he is third on the team with 369 receiving yards.
The unbeaten Chiefs face a crucial AFC West clash against the 8-1 Denver Broncos on Sunday night.