Campaign group Fathers4Justice said one of its members was responsible for damage to a portrait of the Queen, in an apparent "Father's Day protest".
A spokesman said it was not an official protest.
Painted by Australian-born Mr Heimans, the piece measures 9ft by 11ft and depicts the monarch in the Sacrarium of Westminster Abbey, also known as the Coronation Theatre.
The painting is entitled The Coronation Theatre, Westminster Abbey: A Portrait of Her Majesty Queen Elizabeth II.
It was shown publicly for the first time in September by the Australian governor-general Quentin Bryce at the National Portrait Gallery in Canberra.
It was moved to London and put on display in Westminster Abbey last month.
More top news
Tonight it'll become dry and clear for most parts of Britain.
More than 30 lions rescued from circuses in South America have arrived in Johannesburg to begin a new life at an African wildlife reserve.
A pensioner who made neighbours' lives a misery, including displaying images of Miss Piggy to torment an overweight woman, has been jailed.