Greenpeace says four climbers scaled the towering construction crane about 5.30am on Tuesday and unfurled a 25-metre banner reading "Stop Woodside".
Emergency services were called to the building site in the CBD and arrested three men and a woman, with work resuming at the site by 7.15am.
Woodside described the incident as a cheap and unlawful publicity stunt that put the community at risk and wasted the time of first responders, saying such disruptions won't solve global warming.
Greenpeace says fossil fuel companies like Woodside are Australia's biggest climate threat. (HANDOUT/GREENPEACE)
Greenpeace Australia Pacific chief executive David Ritter defended the action saying "Woodside is Australia's greatest climate threat".
"Woodside threatens our oceans, threatens our whales, threatens our climate," he told reporters after the protest.
The protest comes days after the federal offshore oil and gas regulator gave Woodside the go-ahead to start undersea survey work for its $16.5 billion Scarborough gas project off the WA coast.
Mr Ritter said the operation involves "seismic blasting" and "blowing up" the ocean, which in turn endangers whale habitat.
Gas from the project will be processed at Woodside's Burrup Peninsula onshore facility, where expansion work is underway.
Mr Ritter said it was Australia's "most climate polluting" project and could "spew out" up to 6.1 billion tonnes of carbon emissions over its 50-year life.
"Bigger than the combined total of the next two largest proposed fossil fuel projects in Australia," he said.
The environmental lobby group wants the federal government to reject Woodside's Burrup Hub Proposal.
"Right now, in Dubai, world leaders are hearing yet again from climate scientists that it is essential that the world transitions away from coal, oil and gas at emergency speed and scale, which is the very opposite of what Woodside is planning," Mr Ritter said.
A Woodside spokeswoman said the company was proud of its contribution to the national economy.
"Our Scarborough Energy Project will create more than 3000 jobs in the construction phase and add almost 600 new operational jobs," she said.
The Burrup Peninsula, about 30km west of Karratha in WA's Pilbara region, is also known as Murujuga to traditional owners and contains the world's largest and oldest collection of petroglyphs.
The Scarborough gas field is located in the Carnarvon Basin, about 375 km off its coast.
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