Climate activists targeted the British Open on Friday, setting off a smoke flare and throwing orange powder onto the Royal Liverpool course before being arrested.
The Just Stop Oil group said it was responsible for the demonstration at the 17th hole on the second day of action at Hoylake.
Police confirmed that four people had been arrested.
British golf's landmark tournament is the latest high-profile sporting event to be targeted by Just Stop Oil in recent weeks following interruptions at Wimbledon and during the second Ashes cricket Test at Lord's.
"At around 12.20 pm three Just Stop Oil supporters ran onto hole 17 at The Open in Royal Liverpool," the group said in a statement.
"They set off a smoke flare and threw orange powder paint on the green before being removed by security."
American golfer Billy Horschel escorted a woman wearing a Just Stop Oil T-shirt away from the putting surface and towards a police officer.
Another woman and two men, wearing similar T-shirts, were also handcuffed and marched off the course by several police officers.
Police said in a statement that "a small amount of powder was discarded onto the playing surface and it was reported that one person had a smoke pyrotechnic".
They added: "Two males and two females were quickly detained by both stewards and officers and they were arrested on suspicion of conspiracy to commit criminal damage and public nuisance. They will be taken into police custody to be questioned."
Greenkeeping staff were dispatched to the hole and removed the powdered paint with leaf-blowers.
Tournament organisers the R&A said: "A protester was quickly apprehended on the 17th hole and is one of four people who have been arrested by police.
"Play was not disrupted and we would like to thank the marshals, players and other spectators for their vigilance and understanding as the protesters were removed."
Open organisers were prepared for protests this year and had strengthened security.
They had advised players not to engage with anyone who entered the course but Horschel decided against that.
Just Stop Oil wants the UK government to end all new oil and gas exploration and has promised not to let up in its protests until it does so.
New legislation gives police greater powers to stop and search protesters for items such as padlocks and superglue, as well as arrest people suspected of attempting to cause a public nuisance.
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