The painting went on display earlier this month in Chapter House in the abbey
A portrait of the Queen in Westminster Abbey has been defaced with spray paint, an abbey spokesman has 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.
Campaign group Fathers 4 Justice said it thought a member was responsible but the protest was not official.
The oil on canvas by Ralph Heimans went on display in Chapter House in May and depicts the Queen in state dress.
It was completed last year for the Queen’s Diamond Jubilee celebrations.
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.
A spokesman for the abbey said: “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.”
Buckingham Palace said it would not making any comment on the incident.
The Metropolitan Police said officers were called to the abbey at about 12:30 BST and the arrested man is in custody at central London police station.
In a statement, Fathers 4 Justice said: “This was not an official Fathers for Justice protest but it was carried out by one of our members.
“It’s Father’s Day on Sunday – it’s a very emotional time and this protest was a desperate plea for help.”
The group has run a high-profile campaign for more than a decade for improved rights for men who say they have been denied access to their children.
In 2004 and 2005 members were involved in several high-profile protests, including hurling packages of flour at the then Prime Minister Tony Blair in the Commons and climbing buildings including Buckingham Palace and the Foreign Office dressed as superheroes.
The picture was painted by London-based Australian-born artist Heimans 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 – the area near the altar – of Westminster Abbey.
It was officially unveiled in London in 2012 for the Diamond Jubilee and had been exhibited at the National Portrait Gallery, Canberra until March.
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 2 June 1953.
The most important thing is to get it restored. It will take time but it will be able to be put right again”
Lord HarrisDonor of Ralph Heimans’ painting
The work, purchased for the abbey by Lord and Lady Harris of Peckham, was supposed to remain on public display until September.
Lord Harris told the BBC News Channel he understands turquoise paint had been sprayed “over quite a lot” of the portrait.
“The most important thing is to get it restored. It will take time but it will be able to be put right again,” he said.
He said art experts and Ralph Heimans have now inspected the painting and believe it could be mended in about 10-12 weeks.
Lord Harris said the painting was created in honour of the Queen, who had been on the throne for 60 years and had done so much for the country.
“To take it out on her is ridiculous,” he said.
Speaking last month, Heimans said: “I could not have imagined a more fitting home for my portrait of the Queen than Westminster Abbey, the beauty of which was a great source of inspiration in the conception of the work.
“I am deeply honoured by this acquisition and feel that the significance of the portrait’s narrative will have its strongest resonance in this remarkable setting.”
A spokeswoman for the artist has told the BBC she is still trying to bring Ralph Heimans “up to date” with what has happened to his portrait.