The image was widely shared on social media on Saturday as violent clashes between far-right protesters and police took place in central London.
Scotland Yard said a 28-year-old man was arrested on suspicion of outraging public decency and is currently in custody in Essex after presenting himself at a police station.
Speaking on Saturday in response to the image, Commander Bas Javid said: ‘We are aware of a disgusting and abhorrent image circulating on social media of a man appearing to urinate on a memorial to Pc Palmer.
‘I feel for Pc Palmer’s family, friends and colleagues.
‘We have immediately launched an investigation and will gather all the evidence available to us and take appropriate action.’
Speaking about events on Saturday, Home Secretary Priti Patel said: ‘We have seen some shameful scenes today, including the desecration of Pc Keith Palmer’s memorial in Parliament, in Westminster Square, and quite frankly that is shameful, that is absolutely appalling and shameful.’
MP Tobias Ellwood, who gave first aid to Pc Palmer as he lay dying after being stabbed to death in the grounds of Parliament by Khalid Masood in 2017, said the image of the man urinating next to the memorial was ‘abhorrent’.
Speaking to BBC News, he said the man should come forward and apologise.
When asked whether he thought the urinating man may not have noticed the memorial, Mr Ellwood said: ‘I don’t agree with that at all.
‘This is the gates of Westminster, the most iconic symbol of democracy in the world next to a monument for Pc Keith Palmer.’