He then appears to try to hop onto an airport vehicle, but looks to be refused.
Scrambling for his bag the man breaks into a run and is met by what looks to be two members of airport staff as a plane preparing to take off is seen on the runway behind.
The video - which has been shared thousands of times online - then cuts off. It's been revealed the Bolivian national is now facing a hefty fine.
A Civil Guard spokesman in his destination - a Spanish island off the coast of Africa - said he was stopped when he reached his destination and reported for an airport security infraction.
The spokesman said: "He breached a range of security measures when he saw he was going to miss his flight and despite the efforts of ground personnel to stop him, managed to run across the tarmac as the plane was preparing to taxi out to the runway."
It's believed the man was travelling alone.
A source said: "He wasn't arrested but he was identified so his name could be passed to Guardia Civil officers in Madrid for them to take the appropriate action.
"They didn't manage to identify him in Madrid. The pilot presumably agreed to let him on board because he had a boarding pass but he was lucky not to have been stopped in Madrid because we're currently on terror alert level four and he could easily have been mistaken for a terrorist with all the consequences that come with that."
A spokesman for the Spanish Airports Authority said the unnamed offender had broken a fire alarm in an apparent diversionary tactic.
"It is definitely a first for this airport."
Hundreds of people have commented on the video with one writing: "What did he think was going to happen? That they'd just pull up some stairs and let him board!? Hahaha."
Another joked: "It's just like missing a bus."
A Ryanair spokesman said the security breach is now a matter for Madrid Airport Police.