Smith also pleaded guilty to a charge that he failed to present proof of insurance. He was fined $895.
Smith was arrested on the DUI charge last June. He is subject to a two-game suspension from the NFL because of the guilty plea.
The NFL's substance-abuse policy calls for a two-game suspension for a first offense -- a violation of the law relating to the use of alcohol.
The policy allows for increased discipline for aggravating circumstances, including property damage. Smith was pulled over by police after his car struck and broke a light pole.
Smith, 27, recorded 50 tackles and one interception while starting all 16 games last season, his second with the Chiefs.
The 6-foot-3 Smith has 308 tackles and eight interceptions in six seasons with Kansas City and the Miami Dolphins.