He pointed to Turkey as an example. Turkish President Recep Tayyip Erdogan put a lot of pressure on the central bank to not raise rates to spur credit growth and construction. Now the country is a "disaster" and has extremely high inflation, said Mishkin, an economics professor at Columbia University.
"This is not a good game to play," he said. "Is Trump going to be serious about upping the ante here? If so, that's a problem. But if it is just cheap talk, it will be something that will entertain us and hopefully that will be the end of it."
The central bank is sticking with its plan to gradually increase interest rates because officials think it is the best formula to preserve the economy, according to minutes released Wednesday of the Fed's September policy meeting.
In an interview with Fox Business on Tuesday, Trump acknowledged that the Fed is independent and that he doesn't speak with Powell.
"But I'm not happy with what he's doing, because it's going too fast. Because, you look at the last inflation numbers, they're very low," he said.
Mishkin said the Fed is doing its job properly. So did Richard Fisher, former president of the Dallas Fed.
Fisher, a CNBC contributor, told "Closing Bell" the Fed is the "most steady and important hand in Washington."
"Let the president talk all he wants, but let them conduct policy the way they're conducting it," he said.