Unofficial results showed the proposal to remove his name received nearly 70% of the vote.
The move comes less than a year after authorities in the city opted to change the name of the 10-mile (16km) stretch of road from The Paseo, which it was called since it was completed in 1899.
The Southern Christian Leadership Conference (SCLC) – founded by Dr King, and mostly black civic leaders – battled to have the civil rights icon honoured in this way.
Representatives from both sides of the issue have vowed to find an alternative tribute.
Diane Euston, a spokeswoman for the Save The Paseo group that led the successful petition for the change, said they had been brainstorming for months about ways to pay their respects to Dr King if they won the vote.
Members, many of whom are black, said throughout the campaign that their desire to replace his name was not about race.
Kansas City is 60.3% white and 28.7% black, according to the US Census.
The Save The Paseo group argued the council did not follow proper procedures when it voted in January to rename the road, and did not properly consult residents affected by the change.
During a meeting last week with the city’s mayor Quinton Lucas – who strongly supported having Dr King’s name on the street – members made it clear they intended to be part of that conversation.
He said: “I believe we are going to take positive strides.
“We can in the long run be an example across the nation about what unity is going to look like, what consensus looks like.
“The people have spoken, and people need to continue to speak in a positive manner in order to show Kansas City is an example of the democratic process while continuing to ensure we honour Martin Luther King.”
Mr Lucas, who is black and was on the city council when the name was changed, acknowledged city leaders and the SCLC could have handled the renaming decision better and will learn from the vote.
He said: “Everybody I talked to remains committed to honouring Dr King and his service to the country.
“We have a positive opportunity coming out of this. Every now and then we might need a painful start, but people want to make sure we get it right, that we get the collaboration right.”
Alissia Canady, a former city councillor who was one of the few black leaders to support overturning the name change, said the decision was a “huge opportunity” for the city to be “innovative”.
She added: “We need to have a citywide conversation and be intentional about manifesting King’s dreams, rather than just building another statue or duplicating what others have done.”
Derek Alderman, a geography professor at the University of Tennessee in Knoxville, has studied the naming of streets in honour of Dr King for decades.
It is estimated that there are more than 900 streets named after Dr King in 41 US states.
Professor Alderman claims the next steps are crucial for Kansas City, both to heal from the campaign and to protect its national reputation.
He said: “It’s a good sign that people are wanting to come forward and work with the city, but they need to understand it’s going to require sacrifice.
“It’s not as easy as ‘let’s find a convenient street to name for Dr King.’
“They’ll have to change the identity of a street they’ve known for a long time, with business and property owners to bear some costs, along with hard discussions of racism and exclusion.
“I’m not saying it should be divisive, but it needs to be accompanied with really genuine, hard conversations.