The move is designed to help the project meet construction deadlines set up by the NBA.
Before the vote, council members heard from people on both sides of the issue, including Craig Powell, a critic of the arena financing plan.
"I call on every member of this city council to publicly pledge that you have no intention of consumating that bond sale before the people have a right to vote on June 3rd, provided this thing is qualified."
That "thing" he's referring to is an effort by arena opponents to but the project up for a public vote.
But City Councilman Steve Hansen said keeping the project on track is important.
"Let's keep working hard on this. There's still so much to do and there's a lot of uncertainty. While we have a lot of questions to resolve around community benefits and these other things, we've got a long road. Let's not undermine the project as we go forward. We have a lot of time to refine these answers."
Officials with the Kings say the exemption will also help the team meet its goals for the number of local and small businesses that would be involved in building a new downtown arena. The Kings want at least 60% of the arena work to be done by businesses based in the Sacramento area and 20% by small businesses, figures Councilwoman Angelique Ashby liked hearing.
"I'm excited that this project allows us to do that local component in a real way, in a tangible way and in a very big way for Sacramento. This is about saying to our local chambers, to our local businesses 'you're in and we're going to find a way.'"
The council voted 7-2 in favor of suspending the competitive bidding process.
The Sacramento Kings are revealing more information about their plans for the area around the arena that's now under construction in downtown Sacramento.
The Kings development arm has filed plans with the city's planning commission to be heard at next month's commission meeting.
The Sacramento Kings say the "Farm To Fork" movement will be a big part of the meals served at the new arena downtown.
The City of Sacramento wants to build 137 apartments just down the street from the new arena site.
The lanes have shifted on two heavily-used streets in Downtown Sacramento because of the arena project.
Can you judge a city's economy by how much sewage it generates? The City of Sacramento says requests by new businesses for a special sewer line connection credit have already tripled this year compared to all of last year.
People with affiliations to the group Sacramento Taxpayers Opposed to Pork have filed notice they will appeal a judge's decision denying a request for an injunction blocking the downtown arena project.