Button said the incident happened when his car, which is armoured and driven by a trained undercover police driver, stopped in traffic at a junction about a kilometre away from track.
He has described the driver, Daniel Toni, as "a legend" for the way he barged his way through traffic to get Button out of danger.
Button said: "We left about quarter past seven and headed out of the circuit. About a kilometre away a little bit less, we stopped at some traffic lights.
"We couldn't go through the traffic lights, we were about three cars back. We were in an armoured car with a policeman as the driver, an undercover cop. A great guy.
"He obviously didn't feel that comfortable - he stopped about a car's length behind the car in front. We looked to the right and we saw sort of five or six guys walk out of this building, they were just at the edge of the road.
"They looked a little bit suspicious but I didn't think anything of it until Richard [Goddard], my manager, saw this guy with a sort of baton down his arm.
"I looked across a bit more at the guys and one of them had a gun in his trousers that he was playing with. He looked really uncomfortable, really nervous.
"As soon as I said guns to the driver, he knew what to do. He put it at an angle to the traffic so we could get through and then they started running towards the car.
"There were two guys with small hand guns along with one guy who had a big gun that looked like a machine gun. The driver saw it and floored it.
"There wasn't enough room to get through so we were banging through all the cars, and eventually made it.
"The car wasn't that damaged. We had a problem with the front right suspension but he could keep driving and it was all OK in the end, but not a very nice feeling.
"We couldn't drive fast because the car was damaged and about a kilometre down the road we found a police car.
"We pulled alongside the police car and told them what the problem was. At this point we had two other cars coming up alongside us obviously quite angry because we had damaged their cars.
"As soon as he told them what had happened they were all fine. At the hotel, they got out of their cars and shook the drivers hand because they know what a good job he did."
Button added: "And it wasn't just us yesterday. It was the Sauber guys, and I really feel for them because they actually had to stop the car and give everything over.
"If I didn't have about a hundred cameras in my face, I'd be over it by now. It brings the memories back. But we're lucky, we're all OK. We've just got to hope it was a random attack, because that sort of thing does happen here."
Formula 1 boss Bernie Ecclestone insisted that the incidents should be kept in perspective.
"I have been coming here for 40-odd years, walking about, and I've never, ever had a problem," he said.
"You have to remember we have a lot of problems in England, Oxford Street and places, and in New York people get mugged."