Department spokeswoman Jessica Scaperotti said Tuesday the child was 16 months old. She said the agency does not discuss specific cases. It's not yet known how long the investigation will take.
CBS Station WCBS correspondent Jay Dow reports that the toddler was rushed into the emergency room of Elmhurst Hospital Center around 9:30 p.m. Monday night. The hospital said the little boy had a high fever when he was rushed in.
Less than an hour later, the child died. Now the work begins to determine if it's the city's second fatal case of H1N1 influenza.
On Sunday, a public school assistant principal, Mitchell Wiener, became the city's first swine flu death.
Hospital and city officials say complications besides the virus probably played a part in Wiener's death. But his family has said he suffered only from gout, a joint disease.
"This flu is different from other flus," said New York City Health Commissioner Thomas Frieden. "We don't have a vaccine against it yet. It appears that we don't have a lot of natural immunity to it, at least many people don't."
Anxiety about the flu had led to a sharp increase in walk-ins at Elmhurst by people who have flu-like symptoms, who fear they may have H1N1.
"The wait times in the emergency rooms have tripled or quadrupled," Dr. Luis Rodriguez told WCBS, "just because people are walking in that are not sick, and in the meantime when we get really emergent cases, we have to prioritize, and the staff is now stretched."
Around the country, 46 states now report more than 5,100 cases of the flu.
Worldwide, 40 countries have reported a total of 8,829 confirmed cases, and at least 76 deaths, six in the United States.
On CBS' The Early Show, Dr. Richard Besser, acting director of the Centers for Disease Control and Prevention, said that the flu will continue to spread across the United States, as it has been spreading around the globe.
"It is very important that people understand that every year, seasonal flu can be quite serious," Dr. Besser said. "And individuals who are having respiratory difficulty do need to see their physicians.
"It's important people remember those things we've been talking about that they can do to reduce the likelihood that they'll get sick: Hand washing, covering your cough, and staying home when you're sick."
"It is important that children who are sick stay home, that they stay home for the full period of their illness, and that schools monitor to see whether there are sick children in the school."