A member of the campaign group Fathers 4 Justice is believd to have been responsible for damage.
"This was not an official Fathers for Justice protest," read a statement from Fathers 4 Justice. "But it was carried out by one of our members."
"It's Father's Day on Sunday," the statement continued. "It's a very emotional time and this protest was a desperate plea for help."
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Westminster Abbey confirmed the news of the painting shortly after the damage was carried out.
"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," said a spokesperson for the abbey on Thursday.
"Until work can be done to remedy the damage," they added. "It will, very regrettably, not be possible to have the painting on public view."
To mark the Queen's 60 years on the throne, Ralph depicted the monarch standing on the exact spot where she was crowned in June 1953.
"I wanted to produce a work of particular significance for the Jubilee," said the Australian artist when the painting was unveiled.
"I hope there is a degree of humanity uncommon in traditional Royal portraits. The Queen has an extraordinary aura and a real energy and presence."
Depicted in a solitary moment of reflection in the sacred building where the Duke and Duchess of Cambridge were married, the Queen stands on the recently restored Cosmati pavement which has been the site of every British leader's coronation since the 13th century.