Rome's Court of Appeals referred the case to the European Court of Justice (ECJ), meaning the 43 migrants must now be transferred to Italy, a government source told AFP.
Meloni's flagship plan to outsource migrant processing to a non-EU country and speed up the repatriation of unsuccessful asylum seekers is already being followed closely by Europe.
The plan, heavily criticised by rights groups and opposition parties in Italy, has run into repeated roadblocks, with the ECJ examining legal questions raised by several Italian courts.
The migrants were among a group of 49 people intercepted by Italian authorities as they tried to cross the Mediterranean. They arrived in Albania on Tuesday.
The Court of Appeal's decision is likely to increase tensions between Rome and the judiciary.
Following a separate probe into her role in the release of a Libyan war crimes suspect, Meloni accused parts of the judiciary of politically motivated attacks on both her migrant policies and her leadership.
Galeazzo Bignami, leader of Meloni's Brothers of Italy party in the lower house of parliament, said Friday's decision showed "an attitude of resistance from part of the Italian judiciary" to the government.
But Elly Schlein, leader of the centre-left Democratic Party (PD), said it proved the scheme was "a resounding failure".
Former prime minister Matteo Renzi, head of the Italia Viva party, accused the government of "wasting millions in Albania for an unreasonable, illogical, illegal choice".
And Carlo Calenda, head of centrist party Action, said that "if the judges had not intervened, there would be 43 migrants at a site that is supposed to accommodate 1,500 and costs 800 million. A folly".
Safe countries list
Meloni signed a deal with her Albanian counterpart, Edi Rama, in November 2023 to open two Italian-run centres in Albania.
The centres became operational in October, but judges ruled against the detention of the first two groups of men transferred there.
Like other EU countries, Italy draws up a list of so-called 'safe countries' whose asylum seekers can have their applications fast-tracked.
The judges who blocked the first transfer of migrants cited an ECJ ruling stipulating that European Union states can only designate entire countries as safe, not parts of countries.
Italy's list included some countries with unsafe areas.
In response, Meloni's government passed a law limiting its safe list to 19 countries – down from 22 – and insisting all parts of those nations were safe.
But judges then ruled against a second group of transferred migrants, saying they wanted clarification from the ECJ.
An ECJ hearing has been provisionally set for the end of February, according to Italian media.
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