He was arrested for trespassing on a designated site as he dropped to the ground, police said.
The 21-year-old was not carrying an offensive weapon but inquires are continuing, police added. He has been taken into custody and will undergo a mental health assessment.
No members of the Royal Family are thought to have been at the palace at the time.
It is third time a person has tried to enter the palace grounds this year.
A 22-year-old man was spotted on CCTV in August after climbing over a security fence but he was stopped "within a security perimeter".
Several months earlier, a 41-year-old man spent seven minutes in the grounds before being arrested.
A man has been arrested after climbing over a gate at Buckingham Palace.