The seventh-year cover man was suspended from the league for violating the league's substance-abuse policy after pleading guilty in April on a 2014 DUI charge, the team announced on Friday.
In an odd twist, Smith would have faced a two-game ban, but saw it stretched to three for hitting a street lamp, according to NFL Media Insider Ian Rapoport.
Smith produced a strong season in 2014, finishing as the fifth-best cornerback in the league, according to Pro Football Focus. Starting all 16 games for the Chiefs last season, the 27-year-old cover man allowed just 57 percent of passes thrown his way to be completed.
Smith was a major contributor for a unit that finished second in the league in scoring defense and never allowed a quarterback to throw for 300 yards all season.