A spike in new infections outside China has shattered hopes that the economic fallout could be contained within a few months.
Indonesian markets have been hard hit this month as foreign money exited, with Refinitiv data showing a little more than $340 million in outflows of floating rate notes, greater than those from the Philippines, Thailand or Vietnam, as of Thursday.
On Friday, the rupiah slumped 1.2% to 14,200 per dollar, shares fell more than 4%, and the yield on the benchmark 10-year government bond rose to its highest since mid-January.
"The outlook for the US dollar to Asia still depends on how the Fed interprets the coronavirus, and whether it will take pre-emptive action to arrest the current tightening of financial conditions," said Wei-Liang Chang, a macro strategist at DBS Bank.
For the month, the currency lost 4.5%, its biggest since 2013 and the most among the nine currencies covered in this report.
Malaysia's rinngit shed 0.4% on Friday as investors braced for a meeting of the country's nine monarchs, due later in the day, to determine how the next government will be formed after the shock resignation of Mahathir Mohamad as prime minister.
The currency has lost 3.2% so far in February, on course for its worst month since 2015.
The Indian rupee weakened 0.5%, while the Singapore dollar was down 0.2%.
The Singapore dollar had gained for three sessions prior to Friday's weakness and it may eke out a small weekly gain after five straight weeks of losses as some investors see safety in the city-state's debt.
"We think SGSs (Singapore Government Securities) have scope to outperform peers (other AAAs and USTs) over the medium term," DBS wrote in a note.
"Now Fed rate cut expectations have deepened... the dollar may not be a one-way street," DBS' Chang said, pointing to the Singapore dollar and the Chinese yuan stabilising.
In China, the epicentre of the virus outbreak, the yuan has gained 0.2% for the week but was set to post its first monthly decline in five.
Taiwan was closed for a public holiday.