The risk-sensitive Australian dollar rose 0.37% to $0.7139, recovering after a 1% tumble on Friday that saw it dip to $0.71125 for the first time since Aug 20.
The Canadian dollar also rebounded, with the greenback sliding 0.57% to C$1.2726, off the previous session's two-month high at C$1.2800.
The safe-haven yen , which had been the biggest beneficiary of the flight to quality, slipped 0.25% to 113.75 per dollar. The Japanese currency surged as much as 2% at one point on Friday to 113.05.
The South African rand recovered from Friday's one-year low at 16.3675 per dollar, jumping 0.93% to 16.1400.
South Africa discovered the Omicron variant last week, and countries globally have been quick to tighten border controls with mutations in the spike protein suggesting it could be resistant to current vaccines.
Despite the speed of the response, Omicron has since been detected in places including Australia, Britain, Canada, Germany and Hong Kong.
BioNTech said Friday it may know within two weeks if the vaccine it developed with Pfizer needs to be reworked.
"Until then, market volatility is likely to remain elevated," Rodrigo Catril, a senior FX strategist at National Australia Bank, wrote in a client note. "Markets have been forced to reassess the global growth outlook until we know more."
"We expect currencies to be volatile this week," echoed Joseph Capurso, a strategist at Commonwealth Bank of Australia. "It will not take much negative news about Omicron to push AUD below $0.7000."
President Joe Biden will give an update later on Monday of the US response to the new variant.
The US dollar index - which measures the currency against six major peers - traded at 96.204, after dipping to a one-week low of 95.973 on Friday.
While the dollar stands to benefit from the uncertainty because of its status as a safe haven, it clouds the outlook for when the Federal Reserve - and other global central banks - can raise interest rates.
The euro , which jumped 0.98% on Friday as traders closed out short positions, slipped 0.23% to $1.1290.
Sterling was about flat at $1.3335, off Friday's 11-month low at $1.3278.