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".