A cordon is in place after the man was detained by police at around 19:00 BST on Tuesday after approaching the gates of the palace, Scotland Yard said.
He was arrested on suspicion of possession of an offensive weapon.
There are no reports of shots fired or injuries to officers or the public.
The man was also found to be in possession of a suspicious bag, the Metropolitan Police said.
A controlled explosion was carried out as a precaution after an assessment from specialists.
The King and the Queen Consort were not at Buckingham Palace at the time of the arrest.
Chief Superintendent Joseph McDonald said: “Officers worked immediately to detain the man and he has been taken into police custody.
“There have been no reports of any shots fired, or any injuries to officers or members of the public.
“Officers remain at the scene and further enquiries are ongoing.”
The suspected shotgun cartridges have been recovered and will be examined by specialists.