In the video, the flight captain can be seen asking the elderly man to leave the plane.
When he refused, the captain requested the assistance of the Civil Guard and two officers boarded the plane to escort him off.
After a brief protest, the man removed his case from the overhead locker and left the plane. The man's nationality is currently unclear.
Once he was removed from the flight, it took off and made its way to the island of La Palma with a 20-minute delay.
Passengers recorded the scenes with their phones and uploaded videos to social media.
In a tweet, the airline said: "From Binter we want to express our utmost rejection and outrage at behaviors of this type and show our full support to our crews who constantly strive to provide the best service to our customers."