Officers detained two women and a man on suspicion of criminal damage and disturbance of public order, the Sky News broadcaster reported, citing the police.
The activists climbed onto the ministry's building and unfurled a banner warning about the dangers of bird flu and calling for a halt to animal farming, the report said.
The Animal Justice Project also acknowledged its involvement in the protest, according to the report.
"Courageous climbers have dropped a HUGE 9ft x 15ft banner from the Westminster building, calling on Defra [Department for the Environment, Food and Rural Affairs] to prevent an imminent bird flu pandemic," the organization said on Twitter.
Recently there have been a number of similar incidents involving eco-activists in the UK. Thus, climate activists of the Just Stop Oil movement poured paint over buildings of the Internal Ministry, Bank of England, and others.
Prior to that, activists also threw chocolate cake at the wax figure of King Charles III at Madame Tussauds and poured tomato soup over Vincent van Gogh's painting at the National Gallery in London.