They will also have to show proof in the form of a CDC-issued vaccine card, the New York State Excelsior Pass or the NYC COVID Safe app.
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Even photograph of a vaccination card is acceptable.
Mayor Bill de Blasio has told businesses this will be no different than checking customers' IDs before serving alcohol.
"Just buy into this because it's going to work for all of us, is going to make us all safer," de Blasio said Monday.
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The city is giving businesses nearly a month before it starts enforcing the rule, on September 13, but that doesn't mean there isn't concern about the mandate's impact.
The rules apply to everyone -- customers, employees, New York City residents, commuters and visitors alike -- in settings ranging from arenas to coffee shops to yoga studios. Even strip clubs are included.
There are exceptions for children under 12, who are not yet eligible for vaccination, and athletes, contractors and some performers who don't live in the city.
The policy also excludes church potlucks, community centers, office buildings, house parties - even if they're catered - and people ducking in somewhere to pick up food or use the bathroom, among other exemptions.
The mayor has laid out a fine structure for businesses caught not ensuring indoor customers are vaccinated.
It ranges from $1000 for the first offense, $2000 for the second, and $5000 for the third.
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City officials have promised training for businesses on how to handle possible confrontations between patrons and staffers, who will be on the frontlines of checking vaccination status.
Business owners have offered differing predictions on how their customers will react to the mandate.
The Metropolitan Museum of Art, one of the city's most visited venues, said it was working on how to implement the new rule but supports it.
So does the NYC Hospitality Alliance, a restaurant and bar owners' group, though executive director Andrew Rigie said the vaccine checks add another challenge for establishments struggling to recover from pandemic shutdowns and a labor shortage.
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But restaurateurs hope the requirement will help keep the outbreak from worsening and spurring more onerous restrictions.
The Associated Press contributed to this report.
NYC vax mandate: What you need to visit restaurants, gyms, venues
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