Prince Charles and his wife, the Duchess of Cornwall, were guests of honour at the Sandringham Flower Show in Norfolk when the flap occurred.
Four-year-old Zephyr is the mascot of Army Air Corps.
As Charles and Camilla met with the eagle, a bald eagle named Zephyr, according to the BBC, the eagle appeared to try to get away.
Charles quickly leaned his upper body back and away from the eagle's wings.
In the past the 66-year-old prince was forced to dodge its wings as he handled the bird.
He added: "I'm keeping well back."
When asked whether he would care to give Zephyr a stroke, Charles chuckled cagily and remarked: "You must be joking."
"She would probably take off with me!," he added.
Charles is the patron of the Sandringham Flower Show, held at the Queen's Norfolk Estate.
The show is one of the most prestigious horticultural events in the East of England, attracting thousands of entrants and visitors and raising hundreds of thousands of pounds for charity.
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