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 finished the 2013-14 season with exactly the same record as 2012-2013. But, the team and its fans say it sure feels different.
The City of Sacramento could get as much as a million dollars as the local share of construction-related sales taxes collected for a new arena downtown.
As the demolition date for the portion of the Downtown Plaza where the arena will be built looms, business owners prepare to move or close.
Sacramento's Planning and Design commission have approved plans for the King's downtown arena.
A judge has given Sacramento possession of a former Macy's department store downtown, the last parcel of land needed for the development of a new sports arena.
UPDATE -- A judge delayed his final ruling into the eminent domain case that would allow the city of Sacramento to go ahead with its plans for a downtown arena early Wednesday.
(AP) -- Sacramento's eminent domain lawsuit against the owners of a former Macy's department store downtown will be tried in the city.