Ms Lucas said offering the newly elected President the chance to visit or speak at Parliament sent out “all the wrong signs”.
Mr Bercow won the praise of some MPs on Monday as he told the House of Commons he would strongly oppose inviting Donald Trump to address Parliament.
Speaking on Daily Politics, Ms Lucas said she applauded the Speaker on his stance.
The MP for Brighton Pavilion said: “I think it’s quite right that he challenges the idea that Parliament is there for the Prime Minister to pimp out to whoever she wants to.
Caroline Lucas backed John Bercow's stance on President Trump
Being able to speak in Westminster Hall is a real privilege
“Being able to speak in Westminster Hall is a real privilege.”
Ms Lucas added that May's invite to Trump was “premature” and perhaps would not be as iconic as the Pope’s or, as the first Black US President, Barack Obama’s address to Parliament.
She said: “Really the idea of offering this visit so prematurely and potentially the opportunity to speak in the hall, that’s not been clarified, but potentially, I think absolutely sends out all the wrong signs.”
Mr Bercow spoke out against the US President addressing MPs during a proposed State Visit as a mark of “our opposition to sexism and racism”.
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Trump signs an order to review the Dodd-Frank Wall Street to roll back financial regulations of the Obama era.
The former Tory MP said: “I would not wish to issue an invitation to President Trump to speak in the Royal Gallery.
"As far as this place is concerned I feel very strongly that our opposition to racism and to sexism, and our support for equality before the law and an independent judiciary are hugely important considerations.”
Any parliamentary address from the President would require the approval of the Speaker.
Mr Bercow said he would oppose any possible move to invite Mr Trump in either of the two Houses, which can often host foreign leaders during state visits.