NEW YORK — New York City’s sweeping mandate requiring nearly all private-sector businesses to ban unvaccinated employees from the workplace took effect Monday amid a spike in coronavirus infections.

Workers at roughly 184,000 businesses were required to show proof they have received at least one dose of a COVID-19 vaccine by Monday. Businesses that do not comply could face fines starting at $1,000, but Mayor Bill de Blasio has said imposing penalties will be a last resort.

Employers have to verify and keep a record of each worker’s proof of COVID-19 vaccination. Workers who have only gotten one shot will have to get a second one within 45 days. Companies must display a sign affirming they are complying with the rule “in a conspicuous location,” under the city’s mandate.

The new rules cover private places where work is performed in the presence of another worker or a member of the public. That includes not only stores, but shared work spaces and taxis, according to the requirements.

Businesses are not required to discipline or fire non-compliant workers, but they must keep them out of the workplace. Workers seeking an accommodation on religious grounds can come to work while their request is pending.

Vaccinations are already required in the city for hospital and nursing home workers and for city employees, including teachers, police officers and firefighters. The city also enacted a vaccination requirement for dining indoors at a restaurant, going to a gym or seeing a show.