The man's alleged accomplice, who was waiting on the street outside, was also arrested for conspiracy to commit burglary.
The Queen and the Duke of Edinburgh were not in the Palace at the time as they are currently on their summer holiday at Balmoral.
While Buckingham Palace has not yet commented on the incident, the Metropolitan Police have released a statement saying that both men have been bailed and that a major security review, involving the Home Office and Scotland Yard, will now be carried out in the wake of the event.
"Both men have been bailed to return to a central London police station and enquiries continue," said a police spokesperson. "A review of the specific circumstances of this incident is being carried out.
"No members of the Royal Family were at Buckingham Palace at the time of the incident."
Monday's incident is the worst breach of security at the Palace since 1982 when unemployed father-of-four Michael Fagan climbed up a drainpipe and broke into the Queen's bedroom.
The Queen, who was in bed at the time, spent 10 minutes speaking to the intruder before he asked for a cigarette which allowed her to call a footman, who called the police.
Buckingham Palace is monitored by CCTV and surrounded by a wall and a fence, both of which are covered in anti-climb devices.
The building is also permanently guarded by armed officers from the Royal and Diplomatic Protection Unit and further members of security are also present within the Palace itself.