Bowe, who will miss the season opener against the Tennessee Titans on Sept. 7, issued an apology through the players' association.
“I am extremely sorry that I can’t be on the field for the first game of the 2014 season because I made an error in judgment," the statement said. "I take responsibility for my mistake, and it will not happen again. I hope that my teammates, coaches, and Chiefs fans accept my sincere apology.
"I will be supporting my teammates in week one, and I cannot wait to get back on the field to help us win in week two and beyond as we work towards our goal of winning the Super Bowl.”
Bowe was arrested following a traffic stop for allegedly speeding Nov. 10 on suspicion of possessing two containers of marijuana. He later pleaded guilty to amended charges of defective equipment and littering. Bowe was previously suspended four games for violating the league's policy on performance-enhancing substances in 2009.
The Chiefs had a terse statement on the matter: "Dwayne has been given a one-game suspension by the National Football League. We are disappointed in the situation and will miss him on the field, but we support the league’s decision. The club will have no further comment on the matter."
Bowe has struggled the last two seasons to reach the stellar level he showed in 2010 and '11. He combined for 153 receptions, 2,321 yards and 20 touchdowns. The last two seasons he's combined for 118 catches, 1,474 yards and five touchdowns.
Associated Press and wire reports contributed to this story.