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.
Three Sacramento residents have dropped their lawsuit against the city for allegedly providing "secret subsidies" to the Kings' arena.
UPDATE Aug. 13, 11:52 a.m. - The City of Sacramento has sold $299 million in bonds to help pay for the construction of a new arena in downtown Sacramento.
The City of Sacramento has agreed to hold 15 million emails as part of a lawsuit filed by two people who filed a California Public Records Act Request.
Closing arguments are complete in the trial over whether the city of Sacramento provided an illegal subsidy to the Sacramento Kings ownership group as part of the arena deal.
A lawsuit against the City of Sacramento and the Sacramento Kings has gone to trial.
UPDATE: The Sacramento Kings announced Tuesday morning that their new arena will be named Golden 1 Center after the credit union that is headquartered in Sacramento.
Crews are about one quarter into construction of Sacramento's new downtown arena and are already about halfway done with some key components of the project.