Ten were taken to hospital but others refused treatment.
Emergency vehicles were seen on the runway as it landed. He said the sick people were on what he called the "bottom floor".
Emirates Airline has confirmed that "about 10 passengers" have fallen ill from an unidentified illness on flight 203, direct from Dubai to John F. Kennedy Airport in NY, where the plane is now being held under quarantine. A total of three passengers and seven crew members were transferred to a hospital.
The plane was quarantined and members of the Center for Disease Control and Prevention (CDC) and Port Authority of NY and New Jersey screened all passengers and crew members before they could leave the aircraft.
Initial reports from NBC New York said up to 100 passengers said they felt sick, with sources saying about 18 people had been taken to the hospital.
Emergency Service Unit officers from the Port Authority Police Department and the NYPD joined personnel from the FDNY, the Office of Emergency Management and the federal Centers for Disease Control and Prevention (CDC).More news: Australian John Millman in epic US Open clash with Roger Federer
Emirates airlines, the operator of the flight, initially said in a tweet that about 10 passengers had fallen ill.
All of the passengers from the plane were going to be examined away from the main terminal to make sure that there was not any risk of a contagious disease spreading.
EK203 landed at New York's JFK International Airport just after 9 a.m. Wednesday following a 14-hour flight from Dubai, United Arab Emirates.
Phillips tweeted that the flight stopped in Mecca, which is experiencing a flu outbreak, and "early indications point to that as a possibility".
Rap performer Vanilla Ice, who was a passenger on the jet, tweeted, "This is insane".