Officers were called to the palace’s visitor entrance just before 1pm on Sunday, where the man had already been stopped by security staff.
The man, 38, was arrested on suspicion of possessing a firearm (a Taser) and remains in custody at a central London police station.
On its Twitter page, the Metropolitan Police said the incident was not terrorism-related.
Buckingham Palace declined to comment.
The palace is one of the Queen’s official homes, although she frequently spends time at her other residences.
She is currently at Balmoral Castle in Scotland for her summer break.