The passengers, who flew into Rome's Fiumicino airport, were traced across four regions - Calabria, Campania, Tuscany and Veneto - and placed in precautionary quarantine after a Dutch passenger on their connecting flight later died from the virus.
The ministry said all four remained asymptomatic and were in “good” health as of Sunday.
"I'm fine, I have no symptoms," quarantined passenger Federico Amaretti, 25, from Calabria, told Sky TG24 on Monday.
According to Italian media reports, the others under observation were a man living in the province of Naples, a woman in Florence, and a South African citizen in Padua, Veneto.
They were not aboard the MV Hondius, the Dutch-flagged cruise ship at the centre of the outbreak, but had shared a connecting KLM flight with a passenger who was.
READ ALSO: Covid flashbacks haunt Spain's Canary Islands as hantavirus ship docks
She briefly boarded the Johannesburg-Amsterdam service on April 25th, according to AFP, before being removed prior to takeoff. She died the following day, testing positive for hantavirus posthumously.
The MV Hondius docked in Tenerife on Sunday after Spain's transport ministry imposed its arrival despite objections from the Canary Islands local government.
Three people - a Dutch couple and a German woman - have died following the hantavirus outbreak on board the ship.
Ninety-four passengers of 19 nationalities were evacuated on Sunday and transferred to Tenerife South airport for repatriation flights home, with further flights to Australia and the Netherlands completing the operation on Monday.
Positive cases were confirmed among passengers repatriated elsewhere in Europe.
A French woman placed in isolation in Paris tested positive on Monday, France's Health Minister Stéphanie Rist confirmed.
Twenty-two more French nationals had been identified as contact cases after being exposed to someone with the virus
An American national evacuated from the ship also tested positive for the Andes virus - the only hantavirus strain known to spread between humans - the US health department said on Sunday.
READ ALSO: US and French citizens on hantavirus ship that docked in Spain test positive
No vaccines or specific treatments exist for hantavirus, which is endemic in Argentina, where the ship set sail in April.
But health officials have insisted that the risk for global public health is low and downplayed comparisons to the Covid-19 pandemic.
"There is no risk of a new Hantavirus pandemic. We are not in the same situation as Covid. There is currently no alarm. It is a different virus than Covid, albeit more lethal and with low contagion,” the head of Italy’s Disease Prevention Department, Maria Campitiello, told Rai News.
“Transmission is mainly through saliva, urine, and rodent feces, with only a small amount transmitted through the air and human-to-human. The incubation period is long, so isolation is recommended.”
The World Health Organization recommends a 42-day quarantine and "active follow-up", including daily checks for symptoms such as fever, the UN body's epidemic and pandemic preparedness and prevention director, Maria Van Kerkhove, said in Geneva.
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