Children aged 12 and over are required to show proof of full vaccination to access indoor dining areas and many extra-curricular school activities.
The city is also introducing a vaccine mandate for private-sector workers, the first in the US to take such an action.
Jabs are already mandatory for state employees.
The measures were announced earlier this month by Mayor Bill de Blasio, who mentioned the threat posed by Omicron, which appears to be more contagious but milder than other variants.
Cases of Covid-19 have soared in the city and across the country in recent weeks.
* Workers are required to show they have received at least one dose of a Covid-19 vaccine, a requirement that affects around 184,000 private businesses
* They will then be given 45 days to show proof of their second dose
* Children aged 12 and over must show proof of full vaccination to enter venues including restaurants, cafeterias, coffee shops, fast food restaurants, gyms, fitness centres, pools and theatres
Currently, children aged five to 11 have to prove they have received at least one dose of a Covid-19 vaccine to enter those venues. From 29 January, they will also be required to show proof of full vaccination.
Vaccines are available to all residents aged five and older. According to official data, 71.5% of the city's population have been fully vaccinated, but 20% have not yet received a single dose.
The measures come as the city is planning a scaled back New Year's Eve celebration in Times Square, with everyone required to wear face masks and show proof of full vaccination.
Fewer people will be allowed in viewing areas to allow for social distancing. Normally, the event hosts approximately 58,000 people in viewing areas, according to local officials. But this year there will be around 15,000 people only.
New York state confirmed a record 49,708 new infections on 24 December, and 36,454 new cases were recorded on Christmas Day (25 December) although the number is likely to be higher due to labs being closed because of the holiday.