Dimon later expressed remorse for the comments.
A rebuke from the United States president was perhaps inevitable after Mr Dimon told an event yesterday that was meant to showcase JP Morgan's philanthropy that he thought he could beat Mr Trump in an election.
Dimon quickly clarified that he is not running for president and should not have made the remarks. "I'd fight right back", Dimon said during a panel discussion with ABC News reporter Rebecca Jarvis. "He could punch me all he wants, it wouldn't work with me".
The Republican President, known for his acerbic insults on Twitter, was hitting back at Mr Dimon for saying on Wednesday that he was smarter than Mr Trump and could beat him in a White House race.
But he said Trump made his money through "a gift from daddy", while he "actually earned his money". Proves I wouldn't make a good politician. "I get frustrated because I want all sides to come together to help solve big problems".
Last year, Dimon said it was "almost an embarrassment to be an American citizen traveling around the world and listening to the stupid shit we have to deal with in this country".
Dimon, incidentally, was a member of Trump's strategy and policy forum prior to its disbanding, and he has praised the business-friendly tax cuts that the president signed into law past year.
Later on Wednesday after making those comments, Dimon denied any interest in running for president.