Damian McBride said the then prime minister was preparing for "anarchy " throughout the country if banks shut their doors and cut off people's bank cards.
The discussion of the drastic measures came in the days after the collapse of Northern Rock in 2008 and the night before he announced his public bailout of the banks, fearing a "total meltdown of the financial system of the Western world".
Mr McBride added that it was "extraordinary" to see him "gripped by the danger of what he was about to do".
In an extract of his book, Mr McBride wrote that Mr Brown said to him: "You don't understand...If the banks are shutting their doors, and the cashpoints aren't working, and people go to Tesco and their cards aren't being accepted, the whole thing will just explode.
"If you can't buy food or petrol or medicine for your kids, people will just start breaking the windows and helping themselves. And as soon as people see that on TV, that's the end, because everyone will think that's OK now, that's just what we all have to do.
"It'll be anarchy. That's what could happen tomorrow. I'm serious, I'm serious... We'd have to think: do we have curfews, do we put the Army on the streets, how do we get order back?"
But McBride added that Mr Brown was "convinced that decisive action" had to be taken immediately and said he later thought his actions were comparable to President John F Kennedy and his advisers during the Cuban Missile Crisis in the Cold War.