The man, a 57-year-old Polish national, was left perching on the wing of flight FR8164 as it sat on the tarmac at Malaga airport.
He took his hand luggage with him, but was eventually talked into getting back inside the plane by ground staff worried he was going to jump off the wing.
The man, who was arrested by local police, had allegedly become frustrated when the plane was delayed by almost an hour leaving Stansted Airport on New Year's Day.
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Passengers were then left waiting for another 30 minutes to disembark when they arrived in Spain at around 11pm, with no information to explain the delay.
Fernando Del Valle Villalobos, who was on the flight, told the Mail Online: "This man decided he wasn't going to wait any longer.
"He activated the emergency door and left, saying 'I'm going via the wing'. It was surreal."
A spokesman for Ryanair said: "This airport security breach occurred after landing in Malaga airport on January 1.
"Malaga airport police immediately arrested the passenger in question and since this was a breach of Spanish safety and security regulation, it is being dealt with by the Spanish authorities."