The poll risks turning into a referendum on the far-right leader herself, ahead of parliamentary elections next year.
Meloni's hard-right government wants to change Italy's constitution to separate the role of judges and prosecutors and reform their oversight body.
She says the plan is essential to guarantee impartiality and improve the functioning of Italy's creaking justice system.
It will make it "more modern, more meritocratic, more autonomous, more accountable and above all, free from political constraints", Meloni said in a video this week.
But critics condemn it as a political power grab that fails to address the real challenges, from years-long trials to prison overcrowding.
Elly Schlein, the leader of the centre-left Democratic Party, said it was badly drafted and "weakens the independence of the judiciary".
"We have to vote 'no' because the independence of our judicial system is fundamental," Margherita Rossi, a 21-year-old student who came from Milan to Rome to vote, told AFP.
"There is no turnout threshold: even if only 10 people show up, they'll still be able to change the constitution."
Opinion polls show the two camps are neck-and-neck.
A decisive "No" would be a blow for Meloni, who has led an uncharacteristically stable coalition government since October 2022.
However, she has dismissed suggestions that she might quit if she loses.
"I worry about what they could do after if it is passed," said Francescantonio De Luca, a doctor and officer in the army.
Voting closes at 1400 GMT on Monday, with preliminary results expected later that day.
On Sunday, at noon local time (1100 GMT), the turnout was 14.9 percent, the interior ministry said.
'Execution squads'
The late conservative prime minister Silvio Berlusconi was famous for his battles with the judiciary, who he accused of being left-wing.
Meloni and her ministers have also repeatedly attacked rulings they claim are too lenient, particularly on the issue of immigration.
Their reform has sparked intense opposition within the judiciary, with more than 80 percent of members of Italy's National Magistrates Association staging a one-day strike last year.
The referendum campaign has been hard fought and bitter.
In a public spat last month, Justice Minister Carlo Nordio -- who had called criticism from judges "petulant litanies" -- said the reform would correct a "para-mafia mechanism" within the judiciary.
Giusi Bartolozzi, Nordio's chief of staff, also drew widespread criticism when she said during a talk show that the reform would "get rid of" magistrates who operated like "execution squads".
Too-cosy relations
The most divisive part of the reform involves changes to the Superior Council of the Judiciary (CSM), an oversight and disciplinary body whose members are elected by their peers and parliament.
The reform would divide the CSM into two separate councils, one for judges and one for prosecutors, and create a new 15-member disciplinary court.
Members would be drawn by lots, no longer voted by their peers, with three members of the court chosen by Italy's ceremonial president and three from a list of experienced lawyers approved by parliament.
Criminal defence lawyer Franco Moretti, who heads the "No" campaign, said the new court risked being "the armed wing of politics".
"When needed, it could be used to settle scores with that part of the judiciary that has dared to touch it," he said at a debate this month.
The second part of the reform would prevent judges and public prosecutors from switching between the two functions, addressing concerns that too-cosy relations between the two groups harm defendants.
Critics respond that only a tiny minority change roles. In any case, since 2022 they have only been allowed to switch once, while in the first decade of their career.
Referendums in Italy can be politically perilous.
In 2016, then-premier Matteo Renzi staked his career on a constitutional reform that voters rejected, toppling his government.
This weekend's reform is highly technical and some voters admitted to being swayed more by the politics than the substance.
"Beyond the technical question, both sides have injected so much politics into the debate that in the end it's a political referendum, whether Meloni likes it or not," said Stefano Burchi, a 78-year-old retiree.
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