A growing number of cases this week in countries, including Germany, China and South Korea, that had reported early success in containing the virus and had moved to relax some curbs also weighed on investors' minds.
Consequently, South Korea's currency has declined about 0.5% over three sessions.
"Second wave risk remains real and this could see policymakers adopt more cautious steps ahead in opening up their respective economies," Maybank analysts wrote in a note.
Dismal commentary from the Philippine and Malaysian central banks on their respective economic growth prospects also hit sentiment. The peso and the ringgit dropped 0.1% and 0.2%, respectively. Philippines, which was among Asia's fastest-growing economies before the pandemic, is now on the edge of a recession as its central bank predicted a deeper-than-expected economic contraction for this year due to a lack of demand and investments.
Malaysia, despite recording surprise jump in first-quarter GDP, signalled a contraction in economic growth for three-months ended June.
The Singapore dollar and the Indonesian rupiah traded little changed. The Indian rupee firmed 0.2% after the government announced a 20-trillion-rupee ($265.25 billion) stimulus package, 10% of the country's GDP, to support the economy bruised by a strict weeks-long coronavirus lockdown.