A native of Chicago, Illinois, Minsky was born into a family of Menshevik emigrants from Belarus. His mother, Dora Zakon, was active in the nascent trade union movement; his father, Sam Minsky, was active in the Jewish section of the Socialist party of Chicago. In 1941, Minsky received his B.S. in mathematics from the University of Chicago and went on to earn an M.P.A. and a Ph.D. in economics from Harvard University, where he studied under Joseph Schumpeter and Wassily Leontief.

Minsky taught at Brown University from 1949 to 1958, and from 1957 to 1965 was an Associate Professor of Economics at the University of California, Berkeley. In 1965 he became Professor of Economics of Washington University in St Louis and retired from there in 1990. At the time of his death he was a Senior Scholar at the Levy Economics Institute of Bard College.

Minsky was a consultant to the Commission on Money and Credit while he was an Associate Professor of Economics at the University of California, Berkeley.

Minsky proposed theories linking financial market fragility, in the normal life cycle of an economy, with speculative investment bubbles endogenous to financial markets. Minsky claimed that in prosperous times, when corporate cash flow rises beyond what is needed to pay off debt, a speculative euphoria develops, and soon thereafter debts exceed what borrowers can pay off from their incoming revenues, which in turn produces a financial crisis. As a result of such speculative borrowing bubbles, banks and lenders tighten credit availability, even to companies that can afford loans, and the economy subsequently contracts.

This slow movement of the financial system from stability to crisis is something for which Minsky is best known, and the phrase "Minsky moment" refers to this aspect of Minsky's academic work.

"He offered very good insights in the '60s and '70s when linkages between the financial markets and the economy were not as well understood as they are now," said Henry Kaufman, a Wall Street money manager and economist. "He showed us that financial markets could move frequently to excess. And he underscored the importance of the Federal Reserve as a lender of last resort."

Minsky's model of the credit system, which he dubbed the "financial instability hypothesis" (FIH), incorporated many ideas already circulated by John Stuart Mill, Alfred Marshall, Knut Wicksell and Irving Fisher. "A fundamental characteristic of our economy," Minsky wrote in 1974, "is that the financial system swings between robustness and fragility and these swings are an integral part of the process that generates business cycles."

Disagreeing with many mainstream economists of the day, he argued that these swings, and the booms and busts that can accompany them, are inevitable in a so-called free market economy – unless government steps in to control them, through regulation, central bank action and other tools. Such mechanisms did in fact come into existence in response to crises such as the Panic of 1907 and the Great Depression. Minsky opposed the deregulation that characterized the 1980s.

It was at the University of California at Berkeley that seminars attended by Bank of America executives helped him to develop his theories about lending and economic activity, views he laid out in two books John Maynard Keynes (1975), a classic study of the economist and his contributions, and Stabilizing an Unstable Economy (1986), and more than a hundred professional articles.