WARSAW—This week's collapse of a gold-derivatives business that Polish regulators say was a Ponzi scheme has hit tens of thousands of customers, shaken confidence in the effectiveness of the nation's financial regulation, and is roiling national politics in the European Union's largest emerging economy.

On Monday, the company, Amber Gold, Sp. z o.o., which sold a gold-indexed investment of its own design and offered higher interest rates than banks, said it was halting operations....