Fisher, who was president and CEO of the Federal Reserve Bank of Dallas from 2005 to 2015, said the U.S. economy is booming thanks in part to Trump's push for deregulation and the new tax bill.
But Fisher added that at some point, the business cycle will turn and the U.S. will want to mitigate that downturn.
"I don't understand what the president is doing here," Fisher said in a "Closing Bell" interview.
"You want to be able to prolong the business cycle by easing rates when the time comes after the economy begins to roll over. So it's not in his interest, in my view, to criticize the Federal Reserve."
During an interview with Reuters on Monday, Trump said he wasn't "thrilled" with Fed Chair Jerome Powell's intention to keep raising interest rates and said the U.S. central bank should do more to help him to boost the economy.
In an exclusive interview with CNBC's Joe Kernen that aired last month, Trump expressed frustration with the Fed's moves to raise interest rates and said the central bank could disrupt the U.S. economic recovery. He then criticized Fed monetary policy again in a tweet the next day.
Fed officials have raised interest rates twice this year and have indicated two more are coming before the end of 2018.
Fisher, who served as a member of the Federal Open Market Committee, the Fed's principal monetary policymaking group, said it wasn't "appropriate" for an American president to attempt to influence monetary policy. He said Powell should ignore it.