Markets calmed somewhat on Monday, however, with U.S. stock futures and oil prices rebounding, as investors took a more balanced view, waiting until the impact of the variant becomes more clear.
The U.S. dollar index, which had its biggest one-day drop since May on Friday, was at 91.195 at 1054 GMT, overall unchanged on the day and still close to Friday's levels .
The dollar's status as a safe-haven currency means it can benefit from uncertainty, but it fell on Friday because the Omicron variant was seen as possibly affecting when the Federal Reserve and other major central banks will raise rates.
Euro-dollar one-month volatility hit its highest since December 2020 around 0100 GMT on Monday before dropping back down .
"Friday's move was overdone, but the economic outlook is even more uncertain than it was a week ago," wrote Kit Juckes, head of FX strategy at Societe Generale, in a note to clients.
The euro, which rose versus the dollar on Friday, was down around 0.3% at $1.12815 .
European Central Bank policymakers sought to reassure investors, arguing that the euro zone's economy had learned to cope with successive waves of the pandemic.
Commerzbank's head of FX and commodity research Ulrich Leuchtmann wrote in a client note that the euro had initially benefited from the Omicron variant because of the dovishness of the ECB.
"If Omicron leads to lockdowns and a renewed reduction in economic activity on a global scale all rate hike expectations turn out to be in vain and then they will be priced out again pretty quickly," he said.
"And which currencies will be the relative winners Of course, the ones where rate hikes were never priced in very much in the first place. And those were EUR, JPY and CHF."
Japan's yen steadied and was flat on the day versus the dollar at 113.47 . Euro-yen hit a new nine-month low .
The Swiss franc likewise reversed recent moves. On Friday it had its biggest one-day jump versus the dollar since June 2016, a slightly bigger daily move than at the peak of the first coronavirus-induced market shock in March 2020, but on Monday it was down 0.5% on the day, at 0.92605 .
Analysts said that currency markets would likely remain volatile until the new variant was better understood.
"Vaccine efficacy results with the next two weeks will be the most important headline to watch out for as well as whether symptoms are different from that of other variants," Nomura analyst Jordan Rochester said in a note to clients.
Goldman Sachs said it would not change its economic forecasts on the basis of the Omicron variant until its likely impact became clearer.
BioNTech said on Friday it may know within two weeks if the vaccine it developed with Pfizer needs to be reworked.
Meanwhile, in cryptocurrencies, bitcoin hit a seven-week low on Sunday before picking up. At 1100 GMT, it was at $57,228.88, down around 0.2% on the day. Its all-time high of $69,000 was hit earlier this month
(Reporting by Elizabeth Howcroft; Editing by Ed Osmond and Alison Williams)