The violent row reportedly broke out when one passenger, 61-year-old Jean Ballentine, who was seated by a window seat, attempted to "climb over" a neighbouring passenger, 52-year-old Mary Cannady, as the JetBlue flight from Kingston was taxiing towards a terminal at John F Kennedy Airport.
Ms Cannady then pushed her off, after which Ms Ballentine punched the other woman in the face.
A man seated nearby then allegedly intervened to try and break up the fight but Ms Ballentine slashed him in the arm using an eyebrow shaving razor, according to local authorities.
Ms Cannady was said to have subsequently grabbed a small can of pepper spray from her bag and sprayed the eye-irritant at Ms Ballentine.
The fight forced the pilot to open the aircraft door and order Ms Balletine to be escorted off the plane, said Joseph Pentagelo, a spokesperson for the Port Authority.
Several passengers were treated for breathing issues following the exposure to pepper spray, while the man who was cut by the razor was also treated for his injury.
Ms Ballentine, from Brooklyn, New York, was arrested for assault and the criminal possession of a weapon while Ms Cannady, from Linden, New Jersey, was charged for the unlawful possession of pepper spray, officials said.
The eyebrow razor and pepper spray would not have been allowed on the plane had the flight departed from the US where it is illegal to bring either on board, the Port Authority told the local radio station WCBS 880.
America's Transportation Security Administration (TSA) is not accountable for security outside the US, but the authorities in Jamaica are responsible for checking for weapons at Kingston Airport, CBS New York reports.