The pilot chose to divert to Corpus Christi, Texas, after crew members reported "a potential threat in the cabin", Southwest Airlines said in a statement, noting that the FBI is investigating the situation.
Some passengers claimed that the woman had been behaving strangely at the gate before the flight from Los Angeles.
Passengers on board the flight said a woman attempted to pry open the emergency exit door during the flight.
Due to differences in air pressure, experts say it would be nearly impossible for a passenger to open the door of an aircraft during a flight.
Adriana Bain, another passenger, said she saw a "scuffle" in the back of the plane.
The woman who captured the cell phone video later said the Federal Bureau of Investigation interviewed several passengers about the woman.
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The suspect was ultimately subdued by Pamela Minchew, an off-duty officer from Cleveland ISD in Liberty County, according to Cleveland ISD Police Chief Rex Evans, who said he spoke with Minchew on Sunday evening. Once she identified herself as an officer, passengers began to calm down. "If she hadn't acted so quickly, things could have gone very differently".
"Everybody was just in shock", he said from the Corpus Christi airport, where passengers had been allowed to leave the plane.
The flight carrying more than 170 passengers and crew later continued on to Houston, about four hours behind schedule.
She reportedly wrote the words, "Help me" on beverage napkins.
Video apparently showing the female passenger being removed from the plane has surfaced on Twitter.
The FBI is investigating the incident and the woman is in custody, KRIS local news reported.