The proposal to remove Dr King's name claimed almost 70% of the vote, preliminary results show.
The council voted in January to rename The Paseo, a 10 mile (16km) boulevard in the city's mostly black east side.
The change sparked a fierce battle in the city, with opponents arguing that it had not been carried out properly.
More than 1,000 streets worldwide are said to bear the name of Dr King, with at least 955 found in the US. Kansas City is one of the only major US cities without a street named after the civil rights icon.
Those who wanted Dr King's name removed said they respect his legacy, but criticised the council's decision to push the change through by waiving a requirement that 75% of property owners on the boulevard should approve it.
"I overwhelmingly heard from my constituents that they did not want it," Alissia Canady, who served as councilwoman for the district that encompasses The Paseo, told the BBC. "There were African American property owners that did not agree with this way of honouring Dr King."
Ms Canady, who is black, said the council had been aware that "the political will was not there".
"They rushed to put the signs up with the hope that once the signs were up people would be afraid to take them down. That was the rhetoric: Kansas City can't be the city that takes Dr King's name down," Ms Canady says.
The Kansas City Chapter of the Southern Christian Leadership Conference (SCLC) - an organisation founded by Dr King - led efforts to keep the street's name in his honour. They did not respond to a request for comment.
Rev Vernon Howard, president of Kansas City's SCLC, told The Associated Press news agency that renaming the street Dr Martin Luther King Jr Boulevard was meant to be a symbol for the city's black children.
"Only if you are a black child growing up in the inner city lacking the kind of resources, lacking the kinds of images and models for mentoring, modelling, vocation and career, can you actually understand what that name on that sign can mean to a child in this community," Mr Howard said.
If the sign is taken down "the reverse will be true", he added.
Opponents of the name change set up the Save The Paseo group earlier this year. In April, it gathered enough signatures to put the removal to a vote.
Tensions between the SCLU and Save The Paseo reached a high point last Sunday, when a silent protest was staged at a church rally held by those pushing to keep Dr King's name. Protesters refused requests by pastors to sit down, fuelling accusations of racism.
But Ms Canady, who worked with Save The Paseo, says the charges are "a deflection of what the real issue was".
She continued: "Residents should not be silenced by special interest groups."
"We pushed a reset button," Ms Canady said. "Now everyone has to go back to the drawing board to find a way where we can all celebrate Dr King, and that's a huge opportunity for Kansas City."