The idea is that a large sum of money is wasted on a fool; he does not have the intelligence or drive to invest that money to make it grow or even know how to keep a large money safe.
The version of the expression we use today is first found in Dr. John Bridges' Defence of the Government of the Church of England, 1587: If they pay a penie or two pence more for the reddinesse of them..let them looke to that, a foole and his money is soone parted.