The flight was en route to Honolulu from Los Angeles Jan. 11.
An FBI affidavit said a female passenger identified only as "N.A." told crew members she had been sexually touched by Benjamin David Beyer.
Beyer was in the aisle seat, the woman was in the center seat and the woman's small daughter was in a car seat in the window seat, the affidavit said.
The woman said Beyer smelled of alcohol and offered her some type of pill, which she refused, the FBI said. She said he repeatedly placed his hand in her lap, touching her thigh despite her resistance, as the food cart moved up the aisle.
The woman wrote a note on a napkin and handed it to a flight attendant, who moved Beyer to another seat.
Beyer later said he did not remember any of the incident, the FBI affidavit said.
Though he was questioned and released in Honolulu, he was arrested after a criminal complaint was filed in Hawaii. The FBI said Beyer was taken into custody without incident in Pahoa, Hawaii, and was to appear before a federal judge.