Bedfordshire Police said a 20-year-old man was being questioned about the assault.
King Charles was meeting members of the public outside Luton Town Hall, 30 miles (46km) north of London, when the egg was apparently thrown. He was taken to a different area by his guards and resumed shaking hands with members of the public.
The monarch has traveled Britain since becoming king following the death of his mother, Queen Elizabeth II, in September.
He was due to visit several sites in Luton on Tuesday, including a transit station and a Sikh place of worship, according to the Associated Press.
Last month, a 23-year-old man was arrested after throwing eggs at Charles and his wife, Camilla, during a visit to York in northern England. The man was later released on bail.
A 20-year-old man has been arrested after an egg was allegedly thrown in King Charles’s direction during a walk in Luton. pic.twitter.com/XzmFHRBVZX
— The National (@ScotNational) December 6, 2022