Vince Cable has called for Royal Bank of Scotland (RBS) to be split up, in a letter leaked to the BBC.
Writing to Prime Minister David Cameron and Deputy Prime Minister Nick Clegg, Mr Cable said RBS should be turned into a new "British business bank".
Mr Cable also said the government needed to show "more leadership" in supporting key technologies.
He added that the government lacked "compelling vision".
Writing about RBS, of which the government owns 82%, Mr Cable said: "My suggestion is that we recognise that RBS will not return to the market in its current shape and use its time as ward of state to carve out of it a British business bank with a clean balance sheet and a mandate to expand lending rapidly to sound business."
BBC business editor Robert Peston said this suggestion was "a big point of difference" with the Treasury, which wants RBS to be sold off as soon as possible.
Our business editor added that Mr Cable's letter, dated 8 February, gives a "brutally frank analysis of what he sees as the shortcomings in the government's industrial and economic policies".
Mr Cable also uses the letter to say that the government responds to crises after they have developed, instead of being more strategic and proactive.
Our business editor said: "Whether his colleagues, especially his Conservative colleagues, will welcome the implication that the government is the slave of events, rather than the master of them, is questionable."
Mr Cable, one of the most senior Liberal Democrats in the coalition government, told BBC Five Live that his letter "certainly wasn't a comprehensive attack on the government's economic policies".
He added: "This is an enormous storm made out of something much less.
"I think a great deal about what the government is doing, and what my department is doing."
Downing Street has said it does not comment on leaks, or on correspondence between ministers.
Chuka Umunna MP, Labour's shadow business secretary, said Mr Cable's letter "underlines the extent to which the Department of Business lacks clout and has become marginalised".
He added: "It is becoming increasingly clear that David Cameron and George Osborne have become roadblocks to the modernisation and reform needed to create a more productive economy."
John Walker, national chairman at the Federation of Small Businesses (FSB), said he welcomed "the debate that the business secretary's letter will bring".
He added: "As the FSB has long said - tinkering around the edges will not help.
"We need bold action - such as he suggests on RBS - and as such have called on the government to establish a small business administration to fully champion the needs of small businesses."