Terrell Davis, a Pro Football Hall of Fame member, said he was detained by the authorities on Saturday in California after he “lightly” tapped a United Airlines flight attendant’s arm to ask for a cup of ice — an episode that he said left him feeling “humiliated, embarrassed, powerless and angry.”

Mr. Davis, 51, was traveling from Denver to Orange County, Calif., on a United Airlines flight with his family, he wrote in a statement released by his lawyers. During the flight, Mr. Davis said, his son asked for a cup of ice, and that the flight attendant “either didn’t hear or ignored” his son.

Mr. Davis said he then “lightly tapped” the attendant on the arm to get his attention, and that the attendant shouted, “Don’t hit me,” and rushed to the front of the plane.

“I was confused, as were the passengers in front of me who witnessed the exchange,” Mr. Davis wrote. “I thought nothing of it other than this particular employee was incredibly rude and blatantly wrong in his accusations of me hitting him.”

After the plane touched down at John Wayne Airport in Orange County, F.B.I. agents and local authorities boarded the plane and placed Mr. Davis in handcuffs while he was in his seat “without any explanation,” Mr. Davis said.

In a statement that did not name Mr. Davis, the F.B.I. field office in Los Angeles said that the agency and other local authorities responded to “a report regarding an incident that had occurred aboard a flight” at John Wayne Airport.

“One individual was detained for questioning, was cooperative with law enforcement and was released to continue his travels,” the F.B.I. said.

Mr. Davis said that he was questioned and that the authorities determined that the flight attendant “was inaccurate in his accusations.”

“The traumatizing experience of my two sons, my daughter, and my wife watching me being placed in handcuffs — without due process or any explanation — cannot be undone,” Mr. Davis said.

The flight attendant involved was removed from duty while United Airlines investigates the episode, the airline said in a statement on Monday.

“This is clearly not the kind of travel experience we strive to provide, and we have reached out to Mr. Davis’s team to apologize,” the airline said.

Parker Stinar, a lawyer representing Mr. Davis, said in an email that the episode on the flight was “appalling and disturbing to say the least.”

“We can all agree no person should be subjected to this kind of injustice and humiliation, especially in front of their children and wife,” Mr. Stinar said.

Lawyers for Mr. Davis were investigating what happened on the flight, and were “actively contacting” United Airlines, Mr. Stinar said.

Mr. Davis played running back in the N.F.L. for seven seasons, winning two consecutive Super Bowls with the Denver Broncos. He was inducted into the Pro Football Hall of Fame in 2017.