Party leader Libby Mettam said the interaction and failure to disclose it afterwards was "deeply disappointing" and a "significant failure of judgement".
"I have required and received the resignation of Dr Thomas as the Deputy Leader of the Liberal Party, Leader of the Opposition in the Legislative Council and from his current senior Shadow Ministerial appointments," she said in a statement on Tuesday.
Ms Mettam said she would consider what future role Dr Thomas could play in the shadow ministry over the coming days.
The West Australian newspaper previously reported Dr Thomas had confirmed he used Mr Burke to set up a meeting last month with prominent businessman John Poynton - Â about two weeks before Ms Mettam claimed her party did not accept any connection with Mr Burke.
The state's Liberal and Labor parties have been warring in recent weeks over the former premier and his alleged links for profit to the Cook government.
"I will continue to hold the Cook Labor government to account, especially on integrity and accountability," Ms Mettam said.
"Brian Burke should not profit from government grants, and I will continue to call this out."
Premier Roger Cook said Dr Thomas's demotion showed the WA Liberals were not fit to govern the state.
"If you can't trust the Liberal party with a very basic question, like have you had contact with an individual, then you can't trust them with government," he said.
"They are a shambles. They're dysfunctional."
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