Antonino Vadala, the owner of several companies, had been detained and released earlier this month over the alleged crimes in the reporter's article.
The new detention was based on a European arrest warrant issued by Italy last year over alleged drug trafficking.
"A court in Venice issued an arrest warrant for this person," Andrea Predajnova, spokeswoman for Slovakia's general prosecutor's office, said in a statement.
"The Italian court is demanding the extradition of Antonino V. for prosecution in Italy for a drug offence committed by an organized criminal group with a transnational scope."
Vadala's name was mentioned several times in Kuciak's last unfinished investigative report, which was published after the journalist and his fiancee were found shot dead at their home near Bratislava in late February.
Tributes to Jan Kuciak and Martina Kusnirova in Bratislava. Photo: Alex Halada/AFP
The murders and article have sparked anti-government protests in the EU country of 5.4 million people, dealing a blow to the cabinet of Prime Minister Robert Fico, whose interior minister announced his resignation Monday and whose coalition partner has called for snap elections.
The article raised possible political links to Italian businessmen with alleged ties to Calabria's mafia supposedly operating in eastern Slovakia.
According to Kuciak, the names of several relatives of an Italian named Antonino Vadala with business activities in Slovakia appeared in 2017 in an arrest warrant for 18 members of a gang engaged in smuggling cocaine to Europe for the mafia organisation 'Ndrangheta.
Vadala has denied the claims in statements to Slovak media.