The Supreme Electoral Council (YSK) on Wednesday ordered that individuals sacked by an emergency decree during purges after a 2016 failed coup could not take up their posts despite being elected.
The candidate who came second would be able to serve in the post instead.
President Recep Tayyip Erdogan has often accused the pro-Kurdish Peoples' Democratic Party (HDP) of ties with PKK Kurdish militants, a charge the party denies.
The HDP said the YSK decision affects many candidates who had already been authorised to stand in the ballot by the same electoral council.
HDP MP Mithat Sancar later told reporters that the party "would launch extraordinary appeals" for the vote to be annulled in five districts and towns where the party's victorious candidates in the Kurdish-majority southeast were affected.
The five candidates have not yet received their certificate of election.
The YSK's decision was "a blow against the elector's will, actually a blow against the future of democracy in Turkey," Sancar said, adding the move was unconstitutional.
"This step taken by the YSK is part of a deliberate political conspiracy, nothing else" by the ruling AKP and its coalition nationalist MHP partner, HDP spokesman Saruhan Oluc said earlier on Thursday. "Show respect to the people's will," he said.
Erdogan's AKP won most seats nationwide in the election, but in a setback lost the capital Ankara and was narrowly defeated in Istanbul, though the party said it will challenge those results.
'Pressure from government'
Hundreds of HDP members and around 40 of its mayors are currently in detention, accused by authorities of ties to PKK militants who are fighting a decades-long insurgency in Turkey.
Other HDP officials said there were other candidates impacted including the party's candidate for Diyarbakir's Baglar district, who won with over 70 percent of the vote.
Nearly 100 supporters including HDP officials tried to enter Baglar authority's building in Diyarbakir on Thursday but were stopped by police, an AFP correspondent said. Some HDP members including MPs then held a sit-in protest instead.
There were chants of "the authority is ours, it will be ours" and "the pressures will not deter us" during the protest, the correspondent said.
"There is pressure from the government, it happens every time," Zeyyat Ceylan, HDP candidate for Baglar, said who attended the protest.
"This is a process in which our people's will has been given to another party, to the AKP... Neither we nor our people approve this," Ceylan added.
The candidate who came second in Baglar was from Erdogan's AKP, with 25 percent. In most of the areas affected, the second candidate is from the AKP.
More than 140,000 people were sacked or suspended from the civil service or public institutions after the 2016 failed overthrow of Erdogan, blamed by Turkey on US-based Muslim preacher Fethullah Gulen. Gulen denies Ankara's accusations.
The majority of those sacked including teachers are accused of links to Gulen but several thousand are suspected of Kurdish militant links.
After the failed coup, the government installed local administrators to replace 95 of the 102 municipalities held by pro-Kurdish mayors elected in 2014.
Before the vote last week, Erdogan threatened to do the same again, replacing mayors linked to "terrorism", he said.
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