Button, his father John, manager Richard Goddard, trainer Mike Collier and an armed guard were in a reinforced, bulletproof Mercedes driving back to their São Paulo hotel following qualifying for this weekend's Brazilian Grand Prix at Interlagos.
In stationary traffic as they passed through a shanty town at around 7pm, the group found itself confronted by a gang of up to six robbers brandishing machine-guns. They were saved thanks to the swift reaction of the vehicle's armed Brazilian police driver, who was hired by the team and is specially-trained in avoidance techniques, who was able to forcefully barge his way past five other cars and speed away to safety.
"We were going back from the track and were outside a shanty town and moving slowly on a busy road," the British star said. "I saw a dog come out, which was very cute. The next thing I saw was a man with a gun. I said 'isn't that a gun?' and as soon as I said that, the driver angled the car and floored it. That's when we saw six men, all of them brandishing machine guns."
"I was terrified," he added. "I saw a man with a truncheon and a pistol. I didn't know what was going to happen. The driver just floored it. We must have bounced off about five cars - we were driving over the top of them - but we got out of there. He was an absolute legend."
"We were about three or four minutes away from the circuit when the incident took place," Goddard told the BBC, describing the unsavoury episode as 'quite a frightening situation' and revealing that he had seen around 70 policemen being spoken to by an officer less than 200 metres away from where the ambush happened.
"This gang came out of the favelas (slums). I would suggest there were more than four or five guys, something along those lines, who emerged from a block of flats. I initially saw one guy carrying this piece of wood, a baseball bat kind of thing, but I didn't spot the one who had a gun until someone shouted 'one of them has got a gun'.
"Another one seemed to have a much bigger weapon. The guy pulled the gun out and someone else pulled an even bigger one out and they came running over towards the car. You didn't really have time to think about what was happening - we told the driver 'go, go, go!' and he just floored it.
"Thankfully the Merc was bloody strong and we had a police driver. If we hadn't it would have been potentially a very nasty situation...they certainly weren't carrying handguns. I don't know what would have happened if he hadn't got the car out - it was the quick-thinking of the driver and the strength of the Mercedes that saved us. You hear about these kinds of things in Sao Paulo, and because they don't come home to roost, you don't think about them - but when it almost happens to you, it's fairly worrying."
Brazil's major cities - and the sprawling metropolis of São Paulo in particular - are notorious for their records of violent crime, with parts of the Interlagos circuit very close to shanty towns, where poverty is rife. Muggings around the time of the grand prix are commonplace.
Three years ago members of the Toyota F1 team were attacked at gunpoint in a similar scenario, escaping unscathed despite shots being fired and a group of youths trying to kick in their car windows. Veteran commentator Murray Walker was also once the victim of an attempted ambush in the same area.
"There are parts of São Paulo which are extremely violent, and [the city] has extremes of great wealth and extreme poverty," the 87-year-old told the BBC. "I suspect that's where it happened to Jenson, and naturally the people who are in the favelas see these obviously very wealthy people driving away from the circuit and they know they've got a lot of money, and they know they've got watches and things on them and that's what they're after presumably."
There is always a visibly high armed police presence around the Brazilian Grand Prix, and F1 personnel are routinely advised not to wear their team uniforms to avoid marking themselves out as potential targets. Button reportedly usually drives himself to and from the circuit, but McLaren insisted he be chauffeured by an armed driver - a move that may well have saved the 30-year-old's life.
'Neither Jenson nor the other occupants were hurt,' confirmed a statement released by the Woking-based outfit, adding: 'The São Paulo authorities have also acted efficiently, and will be providing additional security to transfer Jenson and other senior McLaren-Mercedes personnel to the Interlagos circuit for Sunday's Brazilian Grand Prix.'