Friedman died of heart failure in San Francisco, California, near Stanford University where he taught most recently, friends and associates said.
Friedman won the Nobel prize for economics in 1976 and his thinking greatly influenced former US president Ronald Reagan and ex-British prime minister Margaret Thatcher.
President George W. Bush said the United States had "lost one of its greatest citizens".
"Milton Friedman was a revolutionary thinker and extraordinary economist whose work helped advance human dignity and human freedom," he said in a statement.
US Treasury Secretary Henry Paulson paid tribute to "a great scholar, teacher and advisor" who believed in free markets "even when free markets were not very popular".
Friedman's views were shaped by the Great Depression.
In his writings, he blamed the Federal Reserve for choking off the money supply and so turning what could have been a passing recession into a "major catastrophe" for the world.
That view has held