The Centers for Disease Control and Prevention said on Wednesday the infected individual had recently returned from South Africa.
The traveller was fully vaccinated, has displayed mild symptoms so far and is currently self-isolating, the CDC said.
The US plans to impose fresh travel restrictions over the new variant.
International passengers are expected to soon be required to provide a negative test result from within 24 hours of their departure, US media reports have said.
President Joe Biden is expected to announce the stricter testing requirement and possible additional measures on Thursday.
On Monday, the president said he believes the new variant is "not a cause for panic", adding that it was unlikely to result in domestic lockdowns.
While the World Health Organization (WHO) and the US have deemed Omicron a "variant of concern", it is still not clear whether it is associated with more transmission or more risk of evading vaccines.
The US and other countries have already imposed a ban on travel from eight African countries: South Africa, Botswana, Zimbabwe, Namibia, Lesotho, Eswatini, Mozambique and Malawi.
Health experts say the travel restrictions will buy them time to study the new variant, but new reports suggest the Omicron variant may have already been spreading through western Europe when scientists in South Africa detected it last week.
According to the WHO, at least 23 countries have now reported cases of the heavily mutated variant, including the UK, Canada, and several European Union member countries.
At a White House briefing on Wednesday, CDC director Rochelle Walensky said Omicron's emergence "further emphasises the importance of vaccination, boosters and prevention efforts needed to protect against Covid-19".