The suspect was detained on suspicion of breach of the peace following the incident in Canterbury just before 2:20pm, Kent Police said.
One witness claimed police officers held a man to the ground until the royal couple's car was safely inside the gates of the 900-year-old cathedral.
A Kent Police spokesman said the suspect was still in custody tonight.
"Officers at Mint Yard Gate ... intervened when a man allegedly ran at a car which was taking guests to the Archbishop's enthronement ceremony", the spokesman said.
"A 47-year-old man from Whitstable was arrested on suspicion of breach of the peace and is currently in custody", he added.