Right-hander Brian Bruney was tabbed by manager Joe Girardi to start the game instead. A Yankees spokesman said that Girardi was concerned about a looming rain storm that was projected to hit the Kauffman Stadium area shortly after the scheduled 8:10 p.m. ET start time.
If the rain passed and play resumed, the Yankees said, Kennedy would then pitch.
Kennedy, 23, had a shaky first start against the Tampa Bay Rays in his season debut at Yankee Stadium last week, knocked out after 2 1/3 innings. Kennedy, who was to make his fifth Major League start on Wednesday, allowed six earned runs on four hits, walking four and striking out two.
Bruney, 26, had pitched 3 2/3 scoreless innings of relief this season for New York, reporting to camp lighter and in better shape after improving his diet and workout regimen. He last appeared on Monday, tossing a scoreless inning against Tampa Bay.
The start was Bruney's first since he started two games for the Arizona Rookie League D-backs in 2000, his first professional season.
Bryan Hoch is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.