Smith, 28, pleaded guilty in April to a DUI charge in Kansas City. He was given two years of probation.
The Chiefs released a statement Friday saying they "respect and support the league's decision in this matter and will have no further comment on the situation."
The NFL's substance-abuse policy calls for a two-game suspension for a first offense. But 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.
The Chiefs have some depth at cornerback even without Smith, their best player at the position. Phillip Gaines, Jamell Fleming, Marcus Cooper and Ron Parker all started games at cornerback for Kansas City last season. The Chiefs also drafted cornerbacks Marcus Peters(first round) and Steven Nelson(third).
But the Chiefs are scheduled to face, among other quarterbacks, Denver's Peyton Manning and Green Bay's Aaron Rodgerswithout Smith. The Chiefs face the Broncos in Week 2 at Arrowhead Stadium on Sept. 17 (a Thursday night game) and the Packers in Week 3 in Green Bay on Sept. 28 (a Monday night game).
The Chiefs will begin the season Sept. 13 against the Texans in Houston.
Smith is allowed to take part in offseason and training camp activities, including preseason games. After the regular season begins, he can return to the active roster on Sept. 29, the day after the Chiefs play the Packers.