A 27-year-old man has been arrested and is helping Singapore police with its investigations after invading the Marina Bay street circuit during the grand prix.
The safety car was deployed during the race when the man was spotted on the track, and moments later he climbed back over the barriers to safety.
CCTV footage shows the man climbing through a gap in the security fencing on one side of the track between Turns 13 and 14.
Initially he staggers across the circuit before breaking into a jog as race leader Sebastian Vettel flashes past him.
The man then continues to stagger down the track for around 30 metres as the rest of the field drive past before making his escape through another gap in the fencing.
On the arrest, an FIA statement read: "This follows an incident in which an unidentified man gained unauthorised entry to the circuit during the race.
"We are awaiting a full report from the clerk of the course in order to determine the circumstances surrounding this incident."
A number of F1 team principals have also condemned the man's actions.
Red Bull team boss Christian Horner said: "It shouldn't be possible, in reality.
"So I'm sure the FIA, who are responsible for all things safety-wise, will be having a good look at that and how the crowd can be prevented from ending up on the circuit.
"Obviously it's not only dangerous for him, but also very much so for the drivers."
Toro Rosso team boss Franz Tost called the incident "dangerous and absolutely unacceptable".
Mercedes chief Toto Wolff initially joked the man "must have had a couple of beers" before adding: "It was alarming because that could have caused a massive accident.
"I don't know how he got on there. He must have sneaked in somewhere through a marshal's gap, but it was dangerous for the drivers."
Manor sporting director Graeme Lowdon described the incident as "unusual to say the least".
Lowdon told AUTOSPORT: "I don't know what the story is with this guy, but he looked like someone who was making his way home after a big night out.
"I'm sure it was a pretty scary thing for the drivers to come across, but the drivers managed the situation pretty well, and thankfully no-one was hurt."
It is not the first time a track has been invaded as there have been three other notable incidents in recent times.
In the 2000 German Grand Prix at Hockenheim a man crossed the track, while three years later at Silverstone Neil Horan, wearing a kilt and parading a religious banner, ran down the Hangar Straight, forcing oncoming cars to swerve out of the way.
Earlier this year, at the Chinese Grand Prix, a man scaled the catchfencing along the start-finish straight during second practice.
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