Here's what the portrait looked like before the attack. Ralph Heimans painted it last year for the Queen's Diamond Jubilee.
And here's a (blurry, discolored) photo of what it looks like now.
Scotland Yard said a 41-year-old man has been arrested in connection with the incident. From a Westminster Abbey spokesman, via the BBC:
"In an incident at lunchtime today, a visitor to the abbey sprayed paint on the Ralph Heimans portrait of the Queen presently on display in the Chapter House. Until work can be done to remedy the damage it will, very regrettably, not be possible to have the painting on public view."
The 9-by-11-foot painting is called The Coronation Theatre, Westminster Abbey: A Portrait of Her Majesty Queen Elizabeth II.
UPDATE: The Associated Press has more details about the vandal and his motive.
Fathers 4 Justice, a protest group that campaigns on behalf of fathers denied contact with their children, said the arrested man was a member. It said he had written "Help" with paint on the picture in the abbey's Chapter House.
"It was basically a dad that was desperate to see his kids in the run-up to Father's Day," Fathers 4 Justice campaign director Jolly Stanesby said. "He's decided to ask for help."