The protest took place at Mauritshuis art museum in The Hague, Netherlands, on Thursday.
Footage circulated on social media appears to shows the activist glue his face to glass protecting the 1665 masterpiece by Dutch master Johannes Vermeer, while a second man glues his hand to the wall beside the artwork.
The second protester then pours a tin can of unidentified red liquid over the first man, while both can be seen wearing t-shirts reading ‘Just Stop Oil’.
NOW - Attack on Johannes Vermeer's famed "Girl with a Pearl Earring" painting at a museum in The Hague.pic.twitter.com/N9OgTEnYvb
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Their actions were met with outrage from museum visitors, who can be heard shouting “stupid”, “get away from there” and “shame on you”.
One of the men can be heard saying in the footage: “How do you feel when you see something beautiful and priceless being apparently destroyed before your eyes?
“Do you feel outraged? Good. Remember that feeling when you see the planet being destroyed before your very eyes. This painting is protected by glass - it’s just fine. The future of our children are not protected. People in fuel poverty who need to choose between heat and eating are not protected.”
The two men are seen being escorted away by police in another clip.
Dutch police said three arrests had been made at a museum, but provided no details.
Mauritshuis staff said Vermeer’s world-famous artwork was not damaged in the incident.
“The police were notified and three people have been arrested. The condition of the painting was inspected by our restorer. Fortunately, the glass-covered masterwork was not damaged,” the museum said.
The protest came less than two weeks after “Just Stop Oil” activists threw soup over Vincent van Gogh’s painting “Sunflowers” at London’s National Gallery. That painting was also shielded by glass.
It also comes amid a month of daily protests that have caused disruption across London, carried out by Just Stop Oil - a climate acitivist group calling on the Government to halt new oil and gas licenses in the UK.
Just Stop Oil has been approached for a comment.