Frontrunner Zuzana Caputova, 45, was among tens of thousands of protesters who took to the streets of the eurozone country of 5.4 million last year after the killing raised concerns about media freedom and political corruption.
Opinion polls give the environmental lawyer and mother of two a double-digit lead over European Commission vice-president Maros Sefcovic, a 52-year-old career diplomat backed by the ruling Smer-SD party.
Yet, voters could interpret progress in the case as a sign of a functioning government.
"Caputova attracts those who abhor corruption and who are dissatisfied with what they see as an increasingly... self-dealing government," he told AFP.
"Sefcovic appeals to those with a certain satisfaction with the progress of a country which, by many indicators, has not done at all badly over the last decade."
Neither candidate is on track for an outright victory and a run-off vote is expected on March 30.
Journalist Jan Kuciak and his fiancee were gunned down in February 2018, just as he was to publish a story on alleged ties between Slovak politicians and the Italian mafia plus associated irregularities in EU farm subsidy payments.
The double murder and Kuciak's last explosive report, published posthumously, plunged the country into crisis.
Four people were charged last year with the killings.
Kuciak had been investigating Kocner's business activities and had allegedly received threats from him.
"With this announcement, the authorities may have wanted to show just how effectively the state functions, so it could help Sefcovic gain some points," Bratislava-based analyst Grigorij Meseznikov told AFP.
"On the other hand, this could also be a vindication for Caputova, as she is the symbol of change."
Caputova has vowed to restore public trust in the state, running on a slogan of: "Let us stand up to evil".
She is pro-choice and promotes greater rights for same-sex couples, views that may prove disadvantageous in conservative Slovakia.
Maria Pavlova, a 67-year-old from the southern town of Nove Zamky, said "Slovakia is ready to have its first female president."
But fellow voter Milan Perunko believes Caputova does not have what it takes, unlike her main rival.
"Sefcovic is an experienced multilingual diplomat who can immediately represent Slovakia in the world as soon as he's sworn in," the 54-year-old told AFP.
Campaigning on the slogan "Always for Slovakia", Sefcovic is known for his million-dollar smile. A recent social media meme showed him with the caption "PresiDENT".
Though an independent, Sefcovic has Smer-SD backing, which guarantees him some voters but disqualifies him in the eyes of others.
"I wouldn't vote for anyone who supports Fico or is supported by Smer," said Maria, a biology student from the western town of Piestany.
"The Kuciak murder turned Slovakia upside down... Slovakia's still polarised and Smer hasn't changed a bit," she told AFP.
Though the office is largely ceremonial, the president ratifies international treaties, appoints top judges and is the commander-in-chief of the armed forces.
The head of state can also veto laws passed by parliament.
Polling stations close at 2100 GMT.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)