The amendment concerned increased influence for the government over the role of judges. Meloni and the ruling far-right Brothers of Italy party were behind the proposal.
Opponents of the change believe that the proposal entails greater - and negative - political influence over the legal system.
According to the proposal, judges and prosecutors should also not be able to switch roles - which rarely happens.
On Monday afternoon, Meloni said that the bill had failed, since the 'no' side appeared to be getting around 54 percent of the vote.
The referendum result is seen as a major political setback for Meloni and her coalition government.
