Beck posted an apology on his Web site Friday a few hours after the dialogue aired, CNN reported.
"In discussing how President Obama uses children to shield himself from criticism, I broke my own rule about leaving kids out of political debates," Beck said. "The children of public figures should be left on the sidelines. It was a stupid mistake and I apologize -- and as a dad I should have known better."
Beck's dialogue was inspired by a statement Obama made in a news conference Thursday on the BP oil spill in the Gulf of Mexico. The president said his daughter Malia had asked him "Daddy, did you plug the hole yet?"
On air, Beck and his colleagues had Malia asking the president questions like "Why do you hate black people so much?"
There has been no reaction from the White House to Beck's broadcast or apology, CNN said.