Ms Lucas, whose party wants another Brexit referendum, said the aim would be to force a no-confidence vote in Prime Minister Boris Johnson.
She would then hope to form a "national unity government".
This arrangement - when a group of MPs of multiple parties choose to work together and form a government - has not been seen since the Second World War.
In her Guardian comment piece, Ms Lucas - who used to be the Green Party leader - wrote: "We need an 'emergency cabinet' - not to fight a Brexit war but to work for reconciliation.
"And I believe this should be a cabinet of women.
"Why women? Because I believe women have shown they can bring a different perspective to crises, are able to reach out to those they disagree with and cooperate to find solutions."
Under her proposals, the national unity government would "press the pause button" and organise another referendum offering a choice between Remain or the government's Brexit plan, whether that is an agreed deal or no deal.
She added: "This is not an attempt to replace one coup with another.
"A small group of us should not be deciding on Britain's future and that is not what lies behind my initiative.
"But we need to find a way forward that allows the British people to decide which course they want to take."
Among the women she has invited to join her are Labour's shadow foreign secretary Emily Thornberry, Liberal Democrat leader Jo Swinson, Scotland's First Minister Nicola Sturgeon and Conservative MP Justine Greening.The others are: Heidi Allen, Kirsty Blackman, Yvette Cooper, Sylvia Hermon, Liz Saville Roberts and Anna Soubry.
She has asked to meet the 10 women in the coming days.
It's not known whether any of the women have accepted Ms Lucas's invitation.
But her suggestion has attracted widespread discussion on social media, with many people expressing criticism.
Labour's shadow home secretary Diane Abbott tweeted it "won't work... whatever the gender of the participants".
Labour MP Clive Lewis called it a "very interesting proposal", but asked: "Where are the BAME women politicians?"Ms Lucas replied to him, saying she agreed that the list should be opened out further and she would love Ms Abbott to be involved.Certainly her list could match any of the recent male dominated cabinets over particularly the last years for talent and Nicola Sturgeon is not a MP and the SNP have plenty of women in the House of Commons who could fulfil a similar role.
I see no reason why Ms Lucus Cabinet could'n't work together , but I suspect it would not be to easy hard to name a Cabinet of Women Brexiters , who would be only to willing to implement a No Deal.
The implication of Ms Lucus plans is that the failure of Remain MPs to work together is because of gender , but the truth is that when it comes to equality female politicians can be as equally appalling as men