Hazardous materials crews were called to the scene just after 9 a.m. after the plane landed safely.
Emirates flight 203 arrived at JFK from Dubai and was taken to a staging area, where the Centers for Disease Control and Prevention and Port Authority Police awaited its arrival.
She said all other passengers would be allowed to leave the plane shortly.
"I asked the (flight attendant) for a mask before we even took off, but there was none available", one passenger told CNN. The airline says about 10 passengers fell ill aboard the plan and were receiving medical attention "as a precaution".
Images from the airport in NY showed a line of ambulances waiting to check over passengers from the plane.
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The royal couple will be visiting the Commonwealth countries as requested by the countries governments. In addition to Australia, they will be going to Fiji, the Kingdom of Tonga and New Zealand.
Eric Phillips, spokesman for New York Mayor Bill de Blasio, said there were 521 people on board and that it "appears" that some of the ill passengers had come from Mecca, which is experiencing a flu outbreak.
An Emirates superjumbo in NY has been met by ambulances, police and disease control experts after passengers became unwell. Now some people have fevers over 100.
Phillips tweeted at 12:34 p.m. ET that "all the passengers are off and have been evaluated". Then they boarded buses and again waited outside customs for some time before being admitted to the country.
Officials from the Centers for Disease Control and Prevention and the Port Authority police were reportedly responding to the incident.
The Port Authority of NY and New Jersey did not immediately respond to an AFP request to comment.
Passenger Larry Coben tweeted an image of a CDC form on the plane they were required to fill out.