Portions of the incident on Monday were captured on cellphone cameras and subsequently posted online.
Sweets Lawrence said the trouble began almost immediately after passengers boarded the plane.
"She jumped up and she started cursing," Lawrence told CBC News in an interview over Skype, explaining what she saw on the July 30 flight.
The situation escalated when the plane was in the air, to a point where the unidentified female passenger left her seat and brandished a nail file.
"She came up the aisle with the nail file and she was there to and fro with it and everybody was getting agitated because we were all nervous, we were all scared," said Lawrence.
"We had persons literally running from their seats. Kids were crying, big adults were crying, people were horrified."
Lawrence says that the flight attendants did not stop the woman, even after she allegedly tried to enter the cockpit.
"I got up and I said: ‘Somebody needs to tie this woman up,’" Lawrence said.
"And I started asking the flight attendants to get something to tie her up. They said they were afraid."
Caribbean Airlines did not immediately respond to email and phone messages from CBC News, but the passengers say the airline didn't do anything to the woman. She was not arrested when the plane reached its destination, and none of the passengers were hurt.
The Greater Toronto Airports Authority told CBC News that it is the responsibility of the airline to ask for security or police help when there is trouble.
However, Caribbean Airlines made no such request on July 30.
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