Officers were called to Westminster Abbey around 12.30pm today after security guards detained a 41-year-old man.
He was arrested on suspicion of criminal damage and taken to a central London police station where he is in custody, a Metropolitan Police spokesman said.
The portrait, a Ralph Heimans' oil on canvas designed to commemorate the Queen's Diamond Jubilee, had been on display in the Chapter House for a few weeks before it was vandalised with paint.
More top news
Freezing with frost and fog
A ticket holder in Ireland has won tonight's EuroMillions jackpot which was an estimated 88.5 million euro (£76 million), Camelot said.
In an interview with Rolling Stone, Paris also revealed she tried to kill herself multiple times after being raped at the age of 14.