Miller was arrested on suspicion of misdemeanor battery after the plane landed in Boise.
Police say Miller told officers he smacked the boy with the back of his hand because he refused to follow the directions of the flight crew and wanted to get his attention.
Miller is facing battery charges.
Jail records show Miller has been released from police custody, but he couldn't be reached for comment. The two phone listings for Russell Miller in the Boise area were disconnected.
The Associated Press contributed to this story.