"We are now in an early stage of the virus spread in some developed countries, which is concerning because it could dent investments and consumer sentiment," said Margaret Yang Yan, market analyst at CMC Markets Singapore.
The South Korean won dropped 0.4% against the dollar, hitting its lowest in more than two months, as sentiment remained fragile after the country reported 169 new coronavirus cases.
South Korean President Moon Jae-in on Tuesday called the situation "very grave" and said the coming week would be key in the battle to contain the virus.
The Thai baht weakened 0.4% against the dollar. An investor darling in 2019, the baht has seen a sharp reversal of fortune and become Asia's worst performing currency so far this year.
The Indonesian rupiah fell 0.3%, its biggest intraday drop in more than a month.
Indonesia's finance minister warned the virus outbreak could pressure tax collection and widen the fiscal deficit this year, a day after the government unveiled a nearly $750 million stimulus package to protect the economy.
The Chinese yuan eased 0.1%, while the Philippine peso edged higher.
The Taiwan dollar rose 0.2% and was among the few outliers, a day after the parliament approved a $2 billion package to help cushion the impact from the outbreak.
The ringgit weakened as much as 0.2% to 4.241 per dollar as traders kept a close watch on political developments while awaiting a stimulus package to soften the economic fallout from the epidemic.
Malaysia's king met parliamentarians for a second day to try to end political turmoil by finding someone able to form a government or by calling a new election after Mahathir Mohamad's shock resignation as prime minister.
"The ringgit on trade weighted basis may consolidate around current levels until we see further developments on the government and assistance package to deal with Covid-19," said Chu Kok Wei, group head, treasury and markets, CIMB Group.