The First Minister was among those invited to join the group by Caroline Lucas, the only Green MP in the House of Commons. Jo Swinson, the new Liberal Democrat leader, and SNP MP Kirsty Blackman were also on the list.
Ms Lucas said the all-women cabinet could "bring a different perspective" and its aim would be to force a no-confidence vote in Prime Minister Boris Johnson.
The SNP leader said she welcomed any attempt to halt a no deal Brexit.
The Green MP used a column in The Guardian to claim that a national unity government would "press the pause button" and organise another referendum offering a choice between staying in the EU or the government's Brexit plan, whether that is an agreed deal or no deal.
"It was two women, Betty Williams and Mairead Corrigan, who began the Peace People movement during the worst of the Troubles in Northern Ireland; it was two women, Christiana Figueres and Ségolène Royal, who were key to the signing of the Paris climate agreement; intractable problems have found the beginning of resolution thanks to the leadership of women."
Among the women Lucas has invited to join her are Labour's shadow foreign secretary Emily Thornberry, Conservative MP Justine Greening, and Plaid Cymru Westminster leader Liz Saville Roberts.
The First Minister said: “I welcome any attempt to halt a no deal Brexit, regardless of the composition of the cabinet.
“I am clear that a no deal Brexit will be a disaster for Scotland which is why the UK Government must rule it out immediately. We continue with our preparations to protect against the threats from Brexit, but no amount of preparation or funding can completely mitigate all the impacts of leaving the European Union.”
Lucas’ idea was criticised by international trade secretary Liz Truss, who tweeted: “Is there anything more sexist than claiming your gender determines your worldview/behaviour/attitude?”