Mr Palmer wanted to visit WA for meetings with businesspeople, Senator Mathias Cormann and potential 2021 state election candidates for his United Australia Party but was knocked back.
A spokesman told AAP he had commenced a High Court challenge to the border closure and would cite a section of the constitution that stipulates trade between states must be free.
Mr Palmer accused Premier Mark McGowan of “denying Western Australians jobs and prosperity” by refusing to open interstate borders.
“He risks economic shutdown with his gestapo tactics,” the Queensland-based billionaire said in a statement.
Mr McGowan batted away “bullying” from NSW Premier Gladys Berejiklian over interstate borders earlier this week, saying he wouldn’t take advice from the state at the centre of the Ruby Princess debacle.
Meanwhile, Mr McGowan remains under pressure to fully reopen intrastate travel after WA’s 13 regions were slashed to four vast areas on Monday.
State Liberal leader Liza Harvey labelled his stance on intrastate borders “nonsensical”, given Perth residents could cram on to public transport but not visit northern regions or the Goldfields.
“Every day the Premier dithers, another West Australian small business closes its doors,” Ms Harvey said.
“Our tourism industry is on its knees.”
Health Minister Roger Cook said on Thursday federal biosecurity zones had complicated reopening regional borders, but the police commissioner was working with the state solicitor’s office on dismantling them.
Only three active cases of coronavirus remained in WA as of Thursday.