A rolling roof was one of two ballot measures that Jackson County officials put before voters in April.
One included a 3/8-cent sales tax increase to raise at least $425 million to pay for the work to the stadiums at the Truman Sports Complex.
Officials also have withdrawn a resolution to put the project on the August 8 ballot.
"The business community, the political leaders at both the city and county levels, the Royals, and most importantly many of the citizens of Jackson County all showed some support for the rolling roof," said Chiefs owner Lamar Hunt. "(But) it is the Chiefs determination to move forward with the Arrowhead renovations without a roof. Any Kansas City bid for an NCAA Final Four or a Bowl Championship Series college football game will be deferred."