Chief executive Meg O'Neill says "extremist" protesters accompanied by camera crews illegally trespassed on Tuesday morning at her Perth home in the affluent suburb of City Beach.
"This was not a 'harmless' protest," she said in a statement.
"It was designed to threaten me, my partner and our daughter in our home.
"Such acts by extremists should be condemned by anyone who respects the law and believes people should be safe to go about their business at home and at work."
Woodside said the protest was an unacceptable escalation of protest activity that was designed to threaten and intimidate.
It said the group, understood to be Disrupt Burrup Hub, had no interest in engaging in "respectful and constructive debate" about Woodside's activities.
"Illegal protest activity like this only serves to distract from the real work being undertaken to achieve decarbonisation," a spokesman said.
Police confirmed an incident had taken place in City Beach earlier in the day.
"About 6.45am, officers attached to the state security investigation group attended a home in City Beach as part of an ongoing investigation," a spokesman said.
"Two men, aged 34 and 31, and a 19-year-old woman were arrested and are assisting police with their inquiries."
The protest comes a day after a magistrate rejected a police application for an order to stop some of the group's members communicating while on bail for charges related to other protests that targeted Woodside.
Last week Woodside's lawyers sent a lawyer to a Disrupt Burrup Hub campaigner and said the company wants to start civil court action against members of the group.
The Burrup Peninsula, located in Western Australia's Pilbara region and known as Murujuga to traditional owners, contains the world's largest and oldest collection of petroglyphs.
Disrupt Burrup Hub claims Woodside's operations in the area and its proposed expansion are the biggest new fossil fuel project in the country and could produce billion of tonnes of carbon dioxide by 2070.
It has carried out a series of actions against Woodside this year, including releasing stench gas at its Perth headquarter in June, forcing the evacuation of about 2000 staff members.
Woodside responded last week through its lawyers, who sent a letter to a Disrupt Burrup Hub campaigner and said the company wants to start civil court action against members of the group.
Allens law firm said in the document seen by AAP that Woodside had suffered lost productivity and other damage as a result of the group's activities.
It also requested the addressee to hand over evidence about the group and other protesters within seven days to avoid a Supreme Court application being filed.
Disrupt Burrup Hub have been contacted for comment.
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