The monarch was visiting Luton town centre and taking part in a walkabout when the incident occurred, the PA agency reported.
Bedfordshire Police have said that a man in his 20s has now been arrested on suspicion of common assault and was in custody for questioning.
The eggs were thought to have been thrown towards Charles, and he was temporarily steered away from the crowds outside Luton Town Hall by his security staff shortly after arriving in the area.
But he soon returned to shake hands with the public before moving on to the next part of his visit.
The King was also looking around a new Sikh temple and shuttle at the local airport in Luton.
He met with council officials at the town hall too along with volunteers, taking to the balcony to wave to the public below.
The incident came after a 23-year-old man was arrested for also throwing eggs at Charles (and his wife, the Queen Consort) in Leeds on November 9.
None of the eggs struck either of the royals.
Police officers restrained the man on the ground behind temporary fencing at the time, and was heard reportedly saying, “This country was build on the blood of slaves,” and “not my king”.
Others in the crowd shouted over him, “God save the king” and “shame on you” at the demonstrator.
He was later released on bail. Charles and his wife seemed unperturbed by the interruption and continued greeting the well-wishers.