A public official, who allegedly accepted bribes in exchange for registering illegal Chinese immigrants, is among the Italian and Chinese nationals arrested, SKYTg24 reported.
The gang made up to €450,000 in eight months, with around 300 Chinese people paying bribes of between €600 and €1,500 in order to be registered, a police commander told the TV channel, adding that the operation was a "strong and decisive response to the tragedy of a few days ago."
Police are now probing the factory owner and three managers on suspicion of multiple manslaughter, failing to follow safety procedures and exploiting illegal workers.
It was not clear how the blaze started in the factory in the textile town of Prato, just north of Florence, where about 11 workers had been living and sleeping in close quarters on makeshift beds divided into compartments with cardboard.
Rescue workers said one of the victims had smashed a window in a bid to escape, but had been trapped behind security bars. His carbonized body was found with one arm reaching through the shattered glass.
Prato mayor Roberto Cenni called for more to be done to address the working conditions of Chinese labourers in the city.
Prato is officially home to about 17,000 Chinese nationals, according to official data from 2010, but local sources say the real figure is closer to 50,000.
The presence of the Chinese garment workers is not always welcomed in the city, where numerous Italian firms have been forced to shut as they were unable to compete with the immigrants.
Aldo Milone, the town councillor for public safety said earlier this week that 1,200 busineses have been shut down.
But warehouses closed "often pop up again elsewhere under a different name a few months later," he added.
Enrico Rossi, head of the Tuscany region, called on the Italian and Chinese governments to "take measures" against businesses "which are often victims of extortion by Chinese organised crime."
A vigil was held for those who died on Tuesday.