Cases have been found in Canada, and his speech from the White House comes as US travel bans on eight African countries takes effect.
Mr Biden also urged people to get a booster and to wear masks.
He said he does not anticipate any further US travel restrictions or lockdowns at this time.
In remarks on Monday, the president called it "almost inevitable" that the Omicron strain, first reported by South Africa, will be found in the US "at some point".
He added that said vaccine companies are creating "contingency plans" for new vaccines "if needed".
Late last week, the US announced a ban on flights from South Africa, Botswana, Zimbabwe, Namibia, Lesotho, Eswatini, Mozambique and Malawi. Canada, the UK and the EU and other countries have also restricted travel from southern Africa.
In his remarks, Mr Biden said that the ban had bought some time for the US to study the new strain. While the World Health Organization has deemed Omicron a "variant of concern", it is still not clear whether it is associated with more transmission or more risk of evading vaccines.