The rand weakened about 1.5pc to the dollar after South Africa's central bank delivered a surprise 100 basis point rate cut on Tuesday to cushion the economy from the outbreak.
The bank also signalled more action to support the economy, which it now sees shrinking by about 6pc in 2020, due to added disruptions from the virus. South African stocks fell 2.8pc.
Broader emerging markets were also on the backfoot, with the MSCI's stock index shedding about 0.5pc, while currencies fell 0.2pc.
Investors were cautiously looking to the possible opening up of major economies, given that virus cases were seen peaking in the United States and Europe.
However, the pandemic's economic impact is expected to run rampant, with the International Monetary Fund now expecting the global economy to mark its steepest downturn since the Great Depression of the 1930's.
"It is not (yet) clear whether economies will recover quickly or whether it might take longer than assumed so that we are more likely to see an L-shaped recovery as standard. That means the worst might be yet to come, facing the market with an ice bucket challenge," Commerzbank analyst Antje Praefcke wrote in a note.
Russia's rouble fell about 1.2pc, while stocks shed 2.7pc after new coronavirus cases in the country rose at a record daily pace on Wednesday.
Hungarian stocks fell about 4pc, leading losses among their peers, while the forint retreated slightly against the euro.
Chinese stocks fell, while the yuan also retreated after the country's central bank cut medium-term borrowing costs to their lowest level on record, in a bid to increase liquidity in face of the outbreak.
Markets will now turn to the US corporate earnings season for cues on the full impact of the coronavirus outbreak on company results and forecasts.