Authorities announced sweeping restrictions over the weekend for parts of the regions of Lombardy and Veneto. The restrictions affect about 100,000 people, the civil protection agency estimated on Monday.
Tourist attractions have been closed, private meetings have been banned and schools have been shut. People inside these areas are being asked to stay inside and avoid contact with others. The measures also include transport restrictions in some places and the surveillance and quarantine of individuals who may have been exposed to the virus, according to Italy's health minister.
While European officials are still urging for calm and Italian authorities believe that the spread has been contained, the fact that an outbreak of this scale has happened in a European Union member state will spark fears of wider contagion, given the EU's Schengen Area, which allows people in most EU member states to move between countries without border checks.
The majority of the deaths and cases are in Lombardy, not far from Milan, the region's capital and world-famous tourist hotspot. The city was far quieter than usual on Monday morning, with even its famous Gothic cathedral closed to tourists. And even in this major financial capital, the news of the outbreak appeared to trigger a run on some supermarkets.
Beppe Sala, Milan's mayor, said that "rather than dashing to the supermarkets to grab food, perhaps we should spend time looking after the most vulnerable, such as old people, who are particularly at risk."
Petra Dalla Tor, a resident of Milan, told CNN that while some shelves were empty at her supermarket, she was able to stock up on enough supplies to tide her over. "[I've] never seen it before, but I must say that the rest of the supermarket was okay, the empty shelves were only regarding pasta, biscuits, and canned goods. No problem with fresh fruits and vegetables," she said.
"I don't really understand how serious the situation is, so I just wanted to buy something and be prepared for the week," she added. "Masks are unavailable in all the pharmacies and via Amazon it will take a couple of weeks to have them ... people bought all of them and pharmacies run out of stock, I guess. Same with hand sanitizer."
Viktoria Bozukova, a Milan resident, told CNN she had looked for masks in eight shops on Sunday and three on Monday but that all were sold out. "There are no masks and they don't know when they are going to have [them]," she said.
Attilio Fontana, Lombardy's president, has urged residents to stay calm and stop panic-buying, saying "rushing to stock up on food doesn't make any sense. There are enough supplies."
Matteo Marconi, who lives in the small municipality of Castiglione d'Adda, said he had not experienced the same level of supermarket runs reported in Milan.
"The only real queue was at the pharmacy where a civil protection officer regulates the entrances ... for now it feels like a long weekend, but eventually I think it will start to feel like a situation of constraint," he told CNN. "We live by the day. There are very few people around and they wear masks ... We live near the countryside so we can go outside and walk around, but we limit contact with others as much as possible."
Meanwhile in Venice -- capital of Veneto -- the situation is complicated by the fact that the city is in the middle of its annual carnival, one of the largest tourist events in the Venetian calendar. Before it was canceled, it was due to run until Tuesday, which meant an increased number of visitors, putting greater strain on local authorities.
Luca Zaia, the president of Veneto, confirmed on Sunday that there had been several dozen cases in the region, including two in the city of Venice. He said that private and public meetings were banned until March 1.
The people of Venice are letting their frustrations be known. Roberto, who works at a bar in St. Mark's Square, said, "Why are they here? Why aren't we blocking them," while pointing to a group of Chinese tourists. "This could have been avoided if we closed the ports, blocked all flights coming from China, Korea, Japan."
While countries like Germany, Switzerland and Austria are not imposing travel restrictions on people coming from Italy just yet, fears will remain over Europe's ability to contain a crisis like this. The combination of the continent's relatively open borders and a highly infectious virus that experts say can spread without a carrier showing any sign of symptoms means that the potential is there for the situation to worsen in a hurry.