The World Health Organization is now worried about the growing number of cases that have no clear link to the epicentre of the outbreak in China.
"The omens are not particularly good today," said Ray Attrill, head of FX strategy at National Australia Bank in Sydney. "The presumption was that we would see intermediate supply chains quickly reconnected and I think the market's had to go through a period of questioning that logic."
The Chinese, Australian and New Zealand currencies were on the back foot and emerging market currencies were pounded.
The Aussie carved a fresh 11-year low in early trade and the kiwi shed half a percent, before slightly recovering - along with the yuan - with news of four Chinese provinces lowering emergency restrictions.
That easing provided little support elsewhere, however, with the Korean won plunging nearly 1% to a six-month low. Indonesia's rupiah, so far shielded by its relative independence from Chinese trade, tracked the broader selloff in emerging markets, dropping 1%.
Political turmoil in Malaysia added pressure to the ringgit
and sent it 0.7% lower to its weakest since September.
Yet risk aversion, which also saw stocks tumble and gold and bonds rise, offered surprisingly little support to the yen.
After partially recovering last week's drop on Friday, it traded flat at 111.55 per dollar as Asian investors discount its safety value owing to Japan's virus exposure.
"The market reaction to the coronavirus appears to be evolving, beginning to differentiate the currencies vulnerable to the virus from the rest," Barclays analysts said in a note.
"US dollar assets provide relative attractiveness," they wrote. "In fact, our economists forecast no impact on US growth from Covid-19, with relatively few domestic incidents and a low dependency on China's economy."
Against a basket of currencies, the dollar crept back toward an almost three-year peak touched last week, before soft economic data knocked it from its perch on Friday.
It was firmer against the euro at $1.0820 and pound at $1.2942, while the Swiss franc soaked up some safe-haven flows too and rose 0.3% even with the dollar's strength. Against the euro, the franc stands at a four-and-a-half year high.
The coronavirus has killed more than 2,400 people in China, which also accounts for 98% of global diagnoses.
However, the weekend's spread beyond China appears to have caught authorities off-guard.
Italy has halted the carnival of Venice, shut schools, and sealed off affected towns across its wealthy north, but is struggling to find out how and where the virus' spread began.
South Korea is on high alert and battling to stem steep rises in infections - all adding to the already massive disruption to the world's economy.
"From here on, a lot will depend on how fast China can resume production and contain negative implications for supply chains and global economic growth," said Stephen Innes, Asia Pacific Market Strategist at AxiCorp.