The town, in the south of the country, is renowned for its Ottoman-era Old Bridge over the river Neretva, which was destroyed during Bosnia’s war in the 1990s but has since been restored.
It is the most multi-ethnic town in Bosnia, but the Croat and Bosniak communities have been largely separated by the river since the end of the war in which they fought each other.
Mostar has not held an election since 2008 because its Catholic Croats and Muslim Bosniaks were unable to agree on electoral rules.
However, the dispute has been settled thanks to a 2019 court ruling won by Irma Baralija, a teacher who filed a suit against Bosnia at the European human rights court for failing to hold elections in Mostar.
“This is a very emotional day, for us this has already been a victory,” she told Reuters TV, after casting her ballot.
She is standing for the multi-ethnic Our Party in the election.
The voters will choose 35 city councillors from six ethnically-based electoral units and a central city zone.
About 17% of about 100,000 registered voters had cast their ballots by 1000 GMT, obeying measures against the coronavirus pandemic, election authorities said.
The polling stations closed at 1900 (1800 GMT) and the preliminary results are expected around midnight.
The Croat and Bosniak nationalist HDZ and SDA parties have held a firm grip over Mostar for the past quarter century, each governing its own part of the divided town and its separate utilities, postal companies, universities and hospitals.
The city centre is still dominated by buildings damaged during the war and much of the town’s infrastructure is in disrepair.
Many state-owned firms in the town have shut down due to mismanagement and there has been exodus of young people.
“I expect the city to start functioning because so far nothing has been functioning,” said Hedija Hadzic, a woman in her 50s, after casting the ballot. “At least, we’ll get the city council.”