According to the passenger, the pilot called police, who were then able to remove the woman from the plane.
The passenger said she was able to get in her seat and the plane taxied down the runway, but it was quickly stopped.
"We were stopped pretty quickly and the pilot explained it was because the lady was not cooperating with TSA, and she did not have a ticket to any airline at all," the passenger said. "They could not figure out how she even got on the plane."
The passenger said after about an hour, the Transportation Security Administration said the lady did not go through airport security.
"The plane was searched by dogs and TSA agents. Every single passenger had a pat down and all of our bags were searched again," the passenger said.
It is not known how the woman was able to get past to security or how she was able to get on the plane.
Delta released a statement regarding the incident:
"Delta apologizes to customers of flight 1516 for the delay after a person not ticketed for that flight was removed from the aircraft. Security officials then directed precautionary rescreen of everyone onboard. Delta is working with local law enforcement and the Transportation Security Administration on their investigation and we are conducting our own review of this as well."