The man, Abdel Nur, is believed to be at large on the island.
Three other suspects are in custody, accused of conspiring to blow up fuel tanks and pipelines serving the airport, one of the world's busiest.
The suspects include a former cargo worker and an ex-MP for the South American nation of Guyana.
Had the plot been carried out, it could have resulted in unfathomable damage, deaths and destruction
US attorney Roslynn Mauskopf
JFK 'bomb plot' charges
The plot - which is said not to have gone past the planning stages - involved blowing up the airport's fuel tanks and pipeline, US justice department officials said.
One of the arrests was made in New York and the other two took place in Trinidad.
Guyanese citizen Abdul Kadir, a former member of Guyana's parliament, and Kareem Ibrahim, from Trinidad, are in custody in Trinidad and Tobago.
The authorities said both men were associates of Jamaat al Muslimeen, a Muslim organisation behind a coup attempt in Trinidad in 1990.
The former JFK cargo worker was arrested in Brooklyn late on Friday and named as Russell Defreitas, originally from Guyana.
Mr Defreitas was arraigned in New York City on Saturday afternoon, but did not enter a plea.
JAMAAT AL MUSLIMEEN Muslim social group in Trinidad 140 members took part in 1990 coup attempt Stormed parliament and Trinidad and Tobago TV, taking cabinet hostage 24 people died during coup Coup led by Yasin Abu Bakr, former Trinidadian policeman Those jailed for the coup were freed in 1992 Accused of links to criminal gangs
Profile: Jamaat al Muslimeen
He is to be held pending a bail hearing on Wednesday, US prosecutors said.
It was "one of the most chilling plots imaginable," US attorney Roslynn Mauskopf told a news conference.
"Had the plot been carried out, it could have resulted in unfathomable damage, deaths and destruction."
The pipeline is 40 miles (64km) long and carries jet fuel from New Jersey and through the New York boroughs of Staten Island, Brooklyn and Queens.
See a map of the area
The pipeline serves two other airports in the area - LaGuardia and Newark Liberty.
The FBI said the alleged plot never got beyond the planning stages and there was no threat to air safety or to the public, but that the group's intentions were never in doubt.
"One clear signature of this cell was its persistence, they consistently worked to refine their plot," said Mark Mershon of the FBI's New York office.
"They took extensive measures to seek expert advice, finances and explosives."
Airport videotaped
The alleged plot was brought to light when Mr Defreitas recruited an FBI informant to help him in the plan, officials said.
Mr Kadir is one of the three men already arrested
The men conducted surveillance of the airport, including videotaping their targets and downloading satellite images from the internet, officials said.
They said the informant had recorded some of the conversations he had with Mr Defreitas.
"Any time you hit Kennedy, it is the most hurtful thing to the United States," Mr Defreitas said, according to a recording played to reporters.
"To hit John F Kennedy, wow... they love John F Kennedy like he's the man... if you hit that, this whole country will be in mourning. You can kill the man twice."
Landmarks targeted
In another recorded conversation the suspect was alleged to have said: "Even the twin towers can't touch it," referring to the attack on the World Trade Centre in New York City on 11 September 2001 that killed some 3,000 people.
Any time you hit Kennedy, it is the most hurtful thing to the United States
Alleged statement by Russell Defreitas
"This can destroy the economy of America for some time," Mr Defreitas was alleged to have said.
Mr Kadir studied at the University of Guyana and at the Trinidad campus of the University of West Indies, the Associated Press (AP) reported.
Mr Kadir's wife said her husband knew Mr Nur in the 1980s, but the pair were no longer in contact, AP reported.
"We have not seen him for a long time and I would be surprised if my husband has any links with him still," the agency quoted her as saying.
The arrests are the latest in a series of alleged plots targeting American facilities and landmarks.
Six men were arrested last month on charges of plotting to attack Fort Dix army base in the state of New Jersey.
Three people were arrested in July last year outside the US in connection with a plan to suicide bomb the tunnel under the Hudson River connecting Manhattan with New Jersey.
And in June 2006, seven suspects were charged over an alleged plot to destroy the country's tallest building - the Sears Tower in Chicago.
El edificio del vuelo TWA en el JFK.

 El Departamento de Justicia de los Estados Unidos (DDJ) ha reportado que se han hecho cuatro arrestos en un frustrado intento de hacer detonar tanques de gasolina para jets y gasoductos en el Aeropuerto Internacional John F. Kennedy (JFK), en la Ciudad de Nueva York.

Los cuatro arrestados fueron identificados por el DDJ en una conferencia de prensa el sábado como Russell Defreitas, un ciudadano estadounidense proveniente de Guyana, Abdul Kadir, un ciudadano de Guayana y antiguo miembro del Parlamento de Guyana, Kareem Ibrahim, un ciudadano de Trinidad, y Abdel Nur, también un ciudadano de Guyana.

Defreitas, un antiguo empleado empleado de JFK, fue arrestado en Brooklyn, Nueva York. Kadir y Ibrahim fueron arrestados en Trinidad. No se dejó en claro dónde había sido arrestado Nur, pero el DDJ indicó que los Estados Unidos de América iniciarán el proceso de los cargos para los otros tres.

El DDJ alegó que los cuatro hombres comenzaron su plan en enero de 2006 hasta el día en que fueron arrestados. Se reveló que los oficiales del orden público creían que los objetivos a detonar incluían edificios menores, tanques de gasolinas y ductos de nafta en el JFK, que serían destruidos con explosivos.

EL DDJ alegó que los cuatro arrestados "eran parte de una red internacional de musulmanes radicales de los Estados Unidos, Guyana y Trinidad, y utilizaron el conocimiento y contacto de los conspiradores para desarrollar y planear el ataque, y obtener ayuda operacional y capacidad para llevarlo a cabo."

Defreitas viajó de Guyana a JFK para supuestamente dirigir la vigilancia del aeropuerto en cuatro ocasiones en enero de 2007. De acuerdo al DDJ, los cuatro conspiradores "obtuvieron fotografías satelitales del aeropuerto JFK y de sus facilidades de Internet y viajaron frecuentemente entre Estados Unidos, Guyana y Trinidad para discutir sus planes y solicitar la asistencia técnica y en capital de los otros."

La abogada para el Distrito Este de Nueva York, Roslynn Mauskopf, describió la escena como "una de las conspiraciones más escalofriantes que uno se pueda imaginar." Continuó en decir en la conferencia de prensa en Nueva York que "la devastación que se podría haber causado... es simplemente impensable."