Basically, would there be chaos?
Yes; Our monetary system is simply a shortcut.
Say you have five chickens, and need a cow.
- Without money, you need to find someone who has a cow an needs five chickens.
- With money, you sell the chickens for \$100 and buy a cow for \$100.
You can still trade without money; it's just harder. An interesting side effect of this is that it's unlikely a CEO could ever be paid 2000x his employees wages, just because it would be near impossible to trade 10000 chickens for 2000 cows. Without getting into intricacies of taxation and rulership, compensation would be more or less proportional to work done and trade would be for items of equal value.
It would result in a near instantaneous redistribution of wealth.
That being said, it's very hard to operate without currency. What would likely happen is another form of currency quickly replaces it. For example, in the Fallout universe Bottle Caps are the currency, and "Pre-War Money" is more of a curio or antique. An issue could be that one regions currency is not accepted in another, but that happens even now.
Humanity would survive, but our civilization would halt or regress. Only about 10% of money is real, as our entire economy is built around the concept of fractional reserve banking. We would almost certainly go through a period of anarchy. With no money, there's no police, no jails, no mass transportation, no fuel, etc. Major cities would be bloody hell as factions competed for resources. A city the size of NYC or San Francisco can't sustain its population without importing thousands of tons of food and supplies.
Small towns and rural areas would be the least affected. Traditional Amish communities for example would see almost no difference.