The Men in Black III star explained that his son Jaden Smith asked the US President about the existence of extra-terrestrials.
The actor told Chris Moyles: "I was at the White House with my family and we were getting a tour. The night before, Jaden had said to me, 'Dad, I've got to ask the President about aliens'. I was like, 'Dude, that's not cool. Do not ask the President'.
"We get into the situation room, and Jaden gets this look in his eyes. He's like, 'Dad, what's my punishment?' Jaden says, 'Excuse me, Mr President', and this is why he's the President, he stops and looks at Jaden and says, 'Don't tell me, the aliens right?'"
Obama continued: "I can neither confirm or deny the existence of extra-terrestrials but I can tell you if there had been a top secret meeting it would have taken place in this room."
Asked if his son was still grounded following the question, Smith joked: "He's got about eight or nine more months."
Will Smith recently spoke out in support of Barack Obama's pro-gay marriage stance in the US.
Men in Black III debuts in theatres worldwide on May 25. It receives its UK premiere tonight in London (May 16).
Watch the trailer for Men in Black III below: