Brown, who is fighting an election campaign, piled pressure on Wall Street's most powerful bank, accusing it of "moral bankruptcy" over reported plans to pay big bonuses.
Goldman Sachs was charged with fraud by the US Securities and Exchange Commission on Friday over its marketing of a subprime mortgage product. Goldman has called the US lawsuit "completely unfounded" and has vowed to defend itself.
"I want a special investigation done into the entanglement of Goldman Sachs and the companies there with other banks and what happened," Brown told BBC television.
"There are hundreds of millions of pounds have been traded here and it looks as if people were misled about what happened.
I want the Financial Services Authority (FSA) to investigate it immediately," he said.
"I know that the banks themselves will be considering legal action," Brown said, apparently referring to European banks that lost money on the product marketed by Goldman Sachs.
"We will work with the Securities and Exchange Commission in the United States," he said.
A spokeswoman for the FSA declined comment. "We would never confirm or deny we are investigating anybody," she said.
Brown's Labour Party lags in the polls before the May 6 election and a tough stance against bankers is popular with voters angry about high bonuses paid by banks, particularly those that received state bailouts during the financial crisis.
The FSA is operationally independent and the British government cannot order it to launch an investigation.
The civil lawsuit Goldman faces in the United States is the biggest crisis in years for the company that emerged from the financial meltdown as Wall Street's most influential bank.
Goldman shares slid 12.8 percent on Friday, wiping out more than $12 billion of market value.
According to the SEC complaint, Britain's Royal Bank of Scotland paid Goldman $840 million in August 2008 to unwind a position built up by ABN Amro, some of whose operations RBS had acquired.
RBS is 84 percent owned by the British government after a series of bailouts during the financial crisis.
Brown also attacked Goldman Sachs over a report in Britain's Sunday Times newspaper that the bank planned to pay its staff more than 3.5 billion pounds ($5.6 billion) for three months' work, including 600 million pounds to 5,500 London-based staff.
"I am shocked at this moral bankruptcy. This is probably one of the worst cases that we have seen," he said.
"It makes me absolutely determined we are going to have a new global constitution for the banking system ... a global financial levy for the banks, that all countries that are major financial centers pay, and we quash remuneration packages such as at Goldman Sachs," he said.
"If this is proved to be the case, they have got to return that money. I cannot allow this to continue," he said.
