Campaigner 'on Palace balcony'
Jason Hatch, 33, entered the grounds and scaled a wall onto a balcony, said group spokesman Matt O'Connor.
He said the incident was to highlight the court appearance of Patrick Davis, who allegedly staged a flour-throwing protest in the Commons.
Metropolitan Police have cordoned off the area as crowds built up to watch the protest.
Mr O'Connor said: "We've got a guy dressed as Batman who's on Buckingham Palace on a balcony. He legged it past the armed guards."
The protester, standing on a ledge to the right hand side of the main balcony at the front of the palace, unfurled a banner which read: "Super dads of fathers 4 justice".
Also on the banner are the words: "Fighting for your right to your kids".
A Buckingham Palace spokeswoman said: "There's a man there, but it's a police matter. I'm not sure where he is but I can hear him shouting."
The Queen was not at the Palace as she is at Balmoral in Scotland, the spokeswoman added.
John O'Connor, a former Scotland Yard Flying Squad commander, said he was "astonished" that anyone had been able to breach palace security.
"They are more concerned about the changing of the guard than taking security seriously," he told BBC News 24.