Fischer said his resignation will take effect October 13 and cited "personal reasons" for his departure.
Fischer, 73, who has citizenship in both the United States and Israel, joined the Federal Reserve board in 2014 and his term was to expire in 2020.
Fischer's term was set to expire in June 2018 and his tenure on the Fed was slated to end in January 2020.
Fed Chair Janet Yellen said Fisher would be missed.
At MIT in the 1970s, Fischer taught both Ben Bernanke, who decades later became Fed chair, and Mario Draghi, now the president of the European Central Bank.
Golfer Lewis eyeing a win for Houston
She was leading by three with 18 holes to play and closed with a three under par 69 to win by one. "I'm just really excited". She hit a good lag putt and when the three-footer that was left went in, Lewis had won and the money was going to Houston.
In his two-paragraph letter to the president, Fischer hailed the US economy's progress and the Fed's reforms to make the financial system more resilient.
Last month, Yellen spoke at the annual Jackson Hole Symposium, the year's top meeting of central bankers and economists from around the world, and gave an ardent defense of the US government and the Fed's regulatory response to the financial crisis.
Three spots on the seven-member board were already vacant.
Fischer joined the Fed after serving as a governor of the Bank of Israel, from 2005 to 2013, according to BoardEx, a relationship mapping service of TheStreet Inc. His resignation creates yet another opening for Trump to fill at a critical time for the Fed.
"He represented the Board internationally with distinction and led our efforts to foster financial stability", she added. I'm personally grateful for his friendship and his service. Trump has nominated Randal Quarles, an investment-fund manager and former U.S. Treasury official, as Fed's vice chiair of supervision.