It will examine the future operation of Libor, the rate set every day by the British Bankers' Association (BBA), a Conservative Party source said.
He said there should be a banking code of conduct, with bankers "struck off if they do the wrong thing".
Ministers are also considering a review into bankers' professional standards.
No 10 says it has not ruled out an inquiry but ministers have said new regulation is already in the pipeline.
Barclays has been fined £290m ($450m) after a probe into claims that several banks manipulated the Libor rate.
Rogue traders
Chancellor George Osborne has confirmed that HSBC, RBS, Citigroup and UBS are also under investigation.
Labour's decision to call for an inquiry comes after the Financial Services Authority and the US Department of Justice ordered Barclays to pay a £290m fine for trying to manipulate a key bank interest rate and revelations that banks mis-sold specialist insurance.
The Conservative Party source said the independent review into Libor would be established next week to report by the end of the summer.
Mr Miliband said: "There has been no systematic look at the customs and practices of the banking industry. We've got to have an open, independent inquiry with hearings to find out what's going on in the dark corners of the banks.
"Some of it was clearly illegal, but it goes well beyond that. There is a problem with how these people operate. It wasn't just a few rogue traders out of control and no-one knew what they were doing."
Mr Miliband, who is expected to address the issue in a speech to the Fabian Society Annual Conference later, said he hoped an inquiry would be set up with cross-party support and that he hoped for a new code of conduct which was about "probity, honesty, integrity".
BBC political correspondent Gary O'Donoghue said Mr Miliband was "attempting to set the pace" on the issue after a week in which the stock of bankers had fallen to a new low.
He added that while Downing Street had not ruled out an inquiry, David Cameron had yet to be convinced one was needed and that ministers had been stressing the measures already in the pipeline.
These included the separation of bank investment and retail arms and a new regulatory structure.
The TUC and some Tory backbenchers have also called for a probe similar to the Leveson Inquiry, which is looking into the practices and ethics of the press, but the Treasury and the Bank of England have rejected the idea.
The TUC's head of economic and social affairs, Nicola Smith, said a "continual stream of mis-selling and mis-investment products" suggested the UK banking culture was about "feathering their own nest".
"Our worry is really not just this individual case that's come up this week, but the fact that for the last few years these practices have just become embedded in part of the culture of the UK banking system."
'Culture change'
Business Secretary Vince Cable told BBC News he did not have "any strong objection" to an independent inquiry but added: "I'm not sure how it helps."
Some MPs have called for Barclays' chief executive Bob Diamond to resign and Mr Miliband said: "It is pretty clear that change is required at Barclays and it is very hard to see that led by Bob Diamond."
Bank of England Governor Sir Mervyn King said Britain's banks needed a "real change in culture" but ruled out a wider inquiry.
Mr Cameron supported his comments, saying action on accountability, regulation, transparency and behaviour was what was needed.
He said: "The most important thing people want to see is a really concrete set of actions that will help change the culture.
"You don't change culture by changing laws and changing regulators alone, but I think if we can do this in a very clear and considered way then we have a chance of getting this right," he said.
'Fundamental dishonesty'
Lib Dem backbench Treasury spokesman Stephen Williams backed calls for a Leveson-style inquiry, as did former Conservative Chancellor Lord Lamont.
Mark Garnier, a Tory member of the Treasury Select Committee, said a process in which banks were "pulled over the coals" would address public fears.
He said the levelling of the fine on Barclays was a "game-changing moment" because it showed "fundamental dishonesty and systemic and institutionalised behaviour".
But Treasury Minister Mark Hoban told BBC News there had already been a number of inquiries into the banking sector and people wanted "to see action not words".
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