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
Record crowds are at this year's Pride in London parade as people show their support for the LGBT community after the Orlando shooting
After a showery start to the day, parts of Northern Ireland, western Scotland and south-west England will see drier conditions.
England have beaten Australia 44-40 in the third Test in Sydney to seal a 3-0 series victory.