"We are confident that it will not succeed," she told parliament.
"I'm told the action has never been taken in Australia before."
The legislative council late on Thursday approved unprecedented legislation to amend a 2002 state agreement with Mr Palmer's Mineralogy company.
It is intended to have the effect of terminating arbitration between the two parties and stopping Mr Palmer seeking damages against the state.
Mr Palmer earlier claimed a victory over the McGowan government, revealing the Queensland Supreme Court had formally registered his two arbitration awards.
He said this meant WA's "draconian and disgraceful" legislation would now be invalid under the constitution.
Attorney-General John Quigley has previously said any court action between the bill's introduction and assent would be covered by the legislation, which was fast-tracked through parliament with the support of the WA Nationals and Greens.
The Liberal opposition and some crossbenchers had unsuccessfully sought more time to scrutinise the legislation.
Liberal MP Nick Goiran labelled the process a "pathetic charade for democracy".
Mr Palmer and his associated companies Mineralogy and International Minerals are pursuing damages over a 2012 decision by the former Liberal government to not assess his proposed Balmoral South iron ore mine in the Pilbara.
The government has calculated the total claim to be $27.7 billion minus costs, an amount Premier Mark McGowan said would cripple the state.
Mr Palmer is also challenging WA's borders in the High Court, but it emerged this week he had offered to withdraw the bid if officials agreed to move arbitration hearings relating to the damages claim from Perth to Canberra.