The yen posted its steepest daily fall versus the dollar in nearly six months, while the Swiss franc had its largest daily percentage loss in more than a month.
The Japanese currency and Swiss franc tend to benefit in times of global tension, but they typically struggle when risk sentiment improves.
In contrast, commodity-linked currencies such as the Australian and New Zealand dollars along with the offshore Chinese yuan rose, even as the virus remained a threat.
The People's Bank of China (PBOC) has pumped hundreds of billions of dollars into the financial system this week to cushion the potentially adverse economic impact. In the past two days, the PBOC has injected 1.7 trillion yuan ($242.74 billion) through open market operations.
"There was a bit of optimism about the PBoC's injections into the market," said Mazen Issa, senior FX strategist, at TD Securities in New York.
"It's a strong signal that China is willing to support financial markets in that regard to limit the virus contagion.
But this is very short term and doesn't do anything about the supply chain disruptions," he added.
Still, the death toll from the virus epidemic climbed to 427, infecting 20,438 in China. There have been nearly 200 cases elsewhere across 24 countries. Also, the outbreak is expected to have a devastating impact on first-quarter growth, policy sources said.
In afternoon trading, the dollar rose 0.8% against the yen to 109.51 yen, and gained 0.4% versus the Swiss franc to 0.9690 franc.
Gains against the yen and franc helped push the dollar index higher to 97.952, up 0.2% on the day.
In U.S. politics, Democratic Party officials blamed "inconsistencies" for a delay in Iowa's caucus results. A victory by left-leaning Bernie Sanders or Elizabeth Warren could hurt shares and boost safe-haven currencies.
The euro, meanwhile, slipped 0.2% against the dollar to $1.1040.
The Australian dollar rose 0.6% to US$0.6735
The offshore yuan rose against the dollar, which fell 0.3% to 6.9935.
Elsewhere, sterling rebounded from a near-six week low against the U.S. dollar to trade 0.4% higher at $1.3038.
(Reporting by Gertrude Chavez-Dreyfuss; Editing by David Gregorio and Sonya Hepinstall)
By Gertrude Chavez-Dreyfuss