The conservative coalition run by Ms Meloni had hoped that the system could handle as many as 36,000 migrants and refugees a year.
But a ruling on Friday by a court in Rome has now thrown the entire five-year scheme, estimated to cost €670 million (£557 million), into doubt.
The court ruled that the migrants cannot be sent back to Bangladesh and Egypt because they are not safe countries.
Judges ruled that 12 migrants should be taken to Italy.
Four others had already been spared repatriation because they were deemed to be minors under the age of 18 or in a vulnerable physical state.
The court said it had decided not to validate the detention of the migrants “due to the impossibility of recognising as ‘safe countries’ the states of provenance of the people held”.
The Rome court’s ruling was in line with a decision handed down last week by the European Court of Justice (ECJ), which limited the definition of what can be considered a safe country.
The ECJ said that countries such as Egypt and Bangladesh cannot be declared safe unless their entire territory is free of dangers.
The decision by the court in Rome was met with fury by Ms Meloni’s hard-Right party, Brothers of Italy.
“Absurd! The court does not validate the detention of migrants in Albania,” the party wrote on X.
“Politicised judges have decided that there are no safe countries of origin: it is impossible to detain those who enter illegally, it is forbidden to repatriate illegal immigrants.
“They want to abolish Italy’s borders. We will not let them.”