The powers the government took hold of during the crisis must be repealed in order to begin the process of undoing them.
Democrats pointed out that if the bill becomes law, it could halt a host of Covid-19-specific policies and protections.
Senate Majority Leader Chuck Schumer said in a floor speech that the best way to keep schools open and cases low is by staying at the ready.
The White House said it would veto the bill if it reached Biden's desk.
Republicans in the Senate recently used a different method to pass two bills, one of which repeals Biden's vaccine mandates for large corporations. The House is controlled by Democrats. The Supreme Court upheld the rule for health workers despite blocking the mandate for businesses.