Mitchell Wiener, who had worked at an intermediate school in Queens, died Sunday evening, Flushing Hospital Medical Center spokesman Andrew Rubin said.
Wiener had been sick for nearly a week before his school was closed on Thursday. He had been hospitalized and on a ventilator.
The city's first outbreak of swine flu occurred three weeks ago, when about 700 students and 300 other people associated with a Catholic high school in Queens began falling ill following the return of several students from vacations in Mexico, the epicenter of the outbreak.
Five more city schools will close Monday because of concern for swine flu, bringing the total to 11.
City health officials announced Sunday that four Queens public schools and one Catholic school would close Monday for up to five school days. Three of the public schools are in the same building.
Each school had students with flu-like illness last week.
There were no documented cases of swine flu, or the H1N1 virus, at any of the schools, said Jessica Scaperotti, a spokeswoman for the city Department of Health and Mental Hygiene.
The department is monitoring unusual clusters of flu cases as it works to stop the spread of the swine flu virus, she said.
Six schools were closed last week after hundreds of students became ill with suspected swine flu symptoms.
Besides Wiener, no one else in New York City has become seriously ill from the virus.