There were no "pre-set parameters" ahead of the dinner, and Powell was brought into the White House in "somewhat of a covert operation" to avoid creating speculation, Mnuchin said.
The president has been sharply critical of the Fed. He called the Fed's moves to boost rates his biggest threat.
After a meeting last week, the Fed signaled that it planned to pause its rate hikes and would be "patient" before raising rates again. The announcement sparked a huge rally on Wall Street.
Voiced as Powell's recounting of the meeting, the statement said that he and the president discussed the economy in general, did not discuss upcoming monetary policy, and that Powell told the president Fed decisions were "based exclusively on careful, objective and non-political analysis", an odd civics lesson for a chief executive to receive from an appointee.
Powell's comments in this setting were consistent with his remarks at his press conference of last week, the central bank said. It was a casual meeting. "And we enjoyed a wide range of topics with the president in the residence".
The dinner was held "at the President's invitation.to discuss recent economic developments and the outlook for growth, employment and inflation".
"Whilst the president touched on Chinese trade relations and the budget there was nothing new for traders to sink their teeth into", said Jasper Lawler, the head of research at London Capital Group.
The possibility of a face-to-face between Trump and Powell was brought up late a year ago, as a possible effort to clear the air between the two men after Trump, following a December rate increase, asked aides whether he could fire Powell, and Powell said publicly he would not resign if asked.
Mnuchin said that while the dinner was immediately revealed after it took place, there had been something of a "covert operation" to get Powell into the White House without being seen "so it didn't create speculation" about the objective of Powell's visit. Trump often warms to people after meeting them in person, and Powell is well liked on Capitol Hill by Republicans and Democrats.