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.