The woman had to be restrained by other passengers until the flight landed at about 6:45 p.m., Detroit Metropolitan Airport officials told the Detroit Free Press.
"As of now, it appears she did not have any criminal intent, and instead may be suffering from a medical issue. However, this is based on preliminary reports," Erica Donerson, Wayne County Airport Authority spokeswoman, said in a statement.
The flight was operated for Delta by Indianapolis-based Republic Airline.
"We’re aware of an incident which occurred on our Flight 5972 on Monday evening," said Republic Airline spokesman Jon Austin. "While we can confirm that the flight landed without incident and ahead of schedule, we're unable to further comment as this matter is still being investigated. We apologize to any passengers who were affected by this incident.”
The FBI is investigating the incident, Donerson said.
"After conducting an assessment of the incident and in consultation with the U.S. attorney’s office, it was determined no further investigation was warranted and no federal charges would be filed against the passenger," the FBI said in a statement.