"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," a spokesman for the abbey said.
"Until work can be done to remedy the damage it will, very regrettably, not be possible to have the painting on public view," he said.
A 41-year-old man has been arrested on suspicion of criminal damage after being detained by security guards at the abbey, Scotland Yard said.
It was completed last year for the Queen's Diamond Jubilee celebrations.
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The incident comes nine days after the monarch and other members of the royal family attended a service at the abbey marking the 60th anniversary of her Coronation.
The picture was painted by the London-based Australian-born artist after a sitting with the Queen at Buckingham Palace in March last year.
The work entitled The Coronation Theatre, Westminster Abbey: A Portrait of Her Majesty Queen Elizabeth II measures 9ft by 11ft, and depicts the Queen in the Sacrarium of Westminster Abbey.
Westminster Abbey's website says the painting is an "imagined scene set at night... Showing The Queen in a moment of solitary reflection and is an exceptional interpretation of the intricate mosaic patterns of the 13th century Cosmati pavement."
It shows the Queen wearing state dress, including the crimson velvet Robe of State, which she wore to her Coronation on June 2, 1953.
The work, purchased for the abbey by Lord and Lady Harris of Peckham, was supposed to remain on public display until September.