A second activist glued their hand to the wall next to the 1665 work by Dutch master Johannes Vermeer, and an unidentified liquid was thrown, the Mauritshuis museum said.
An unverified video on social media showed two men near the painting, both wearing "Just Stop Oil" T-shirts.
"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.
Earlier this month, 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.
In videos from the Dutch museum posted online on Thursday, one of the men says: "How do you feel when you see something beautiful and priceless being apparently destroyed before your very eyes?"
"That is that same feeling when you see the planet being destroyed," he adds.
The two men in the video were seen being escorted away by police in more footage.
Dutch police said in a statement they had arrested three Belgian men in their 40s for damage to public property and were conducting a forensic investigation. They were being questioned.
A statement sent by a group calling itself part of the "Just Stop Oil collective," said its Belgian activists were responsible and had thrown soup.
"The message is clear: if humanity does not immediately stop using fossil fuels, it will become extinct," it said. "They would never defile a work of art not covered with protective glass."
A representative of Just Stop Oil in Britain said the protest in The Hague had not been coordinated and it had not been involved. The groups said they are not affiliated.
Dutch Junior Minister for Culture Gunay Uslu said "everyone has the right to make a point. But please: leave our shared heritage alone. Attacking defenceless works of art is not the right way."
(Reporting by Toby Sterling and Charlotte van Campenhout; Writing by Anthony Deutsch; Editing by William Maclean, Andrew Heavens and Barbara Lewis)
By Toby Sterling and Charlotte Van Campenhout
