Nasal mist doses of the vaccine began arriving to providers around the country on Monday.
Schwartz says children ages five to nine will receive the vaccine first because they require two doses.
Health department spokesman Jeff Moran says the shipments are a relatively small portion of the 260,000 or so total doses the city will receive by the end of the month.
Meanwhile, health officials say a small number of local providers in New Jersey have received their initial shipments of the swine flu nasal spray vaccine.
The injectable form of the vaccine is expected to begin arriving in the state over the next few weeks.
The Centers for Disease Control and Prevention says demand for the vaccine is so far outstripping supply.