The couple, who are currently expecting their first child together, had flown in from Brazil and were due to catch a connecting flight to Los Angeles.
According to TMZ, an airline greeter allowed the pair to skip part of the security to save time, although they were swiftly taken off the flight when the Transportation Security Administration became aware of the situation, and were screened privately.
The TSA stressed that Kardashian and West were not to blame for the incident, which is believed to have contributed to the plane being delayed by almost an hour.
"An airline employee escorted the two travellers through a non-public area in order to provide expedited access to their domestic flight," the TSA explained.
"In doing so, the airline employee violated security protocols by permitting the travellers to bypass the TSA security checkpoint.
"TSA officials learned of the violation and conducted a private screening of the two passengers in the area of the jetway.
"The passengers were cleared to board their flight, which departed after a delay of approximately 50 minutes. TSA is actively investigating the incident."
An American Airlines rep added that the company is taking full responsibility for the event.
"This was a lapse in judgement by one of our employees," the airline said. "We're working closely with the TSA and speaking to the individuals involved to better understand what happened."
The firm also insisted that part of the reason the flight was delayed was "because a number of connecting bags were delayed getting to the aircraft".
View all of this week's best celebrity pictures - Photo gallery:
Copyright: WENN Gabor Scott/WENN.com