The accident happened at about 2:20 a.m. opposite Terminal A, according to Port Authority Police.
The victim, a 54-year-old resident of Orange, N.J., was struck by a CommutAir plane that was not on the runway at the time.
Ohio-based CommutAir operates flights for United Express.
The injured woman, who works as a cleaner for a private company, suffered a head injury and was hospitalized in critical condition.
Officials say the accident didn't disrupt airport operations.
The airplane was in a maintenance area opposite Terminal A, the Port Authority said.
The cause of the accident remains under investigation.
(The Associated Press contributed to this report.)