The way power is shared in the UK needs to change radically to ensure the union survives "new tensions" created by Brexit, First Minister Carwyn Jones will say in a speech in Chicago.
Otherwise "nothing, up to and including the break up of the UK... would be inconceivable", he will argue.
Mr Jones is touring the United States to promote Welsh business.
The Conservatives called the speech a "betrayal" of the people of Wales that would harm inward investment.
The first minister will say on Friday that while Leave campaigners in the UK government have an "absolute duty" to honour pledges that Wales will not be worse off financially outside the EU, that alone is not enough.
Mr Jones will tell an audience at the Chicago Council on Global Affairs: "I believe the process of withdrawal must be accompanied by a reformed governance of the United Kingdom for the long term.
"There can be no return to the old constitutional status quo, where the United Kingdom was one of the most centralized states in the developed world.
"But we have to embrace the new reality with fresh constitutional thinking if our British Union is to survive the new tensions created by EU exit.
"Unless we take this seriously, nothing - up to and including the break up of the UK into its component parts - would be inconceivable."
'Needless harm'
Mr Jones will say the UK's disintegration is not something he wants, but will stress "scenarios that seemed little more than political fantasies a few years ago could become plausible if we fail to make the radical changes necessary to put the UK's constitution on a sustainable footing".
In June, he suggested there could a new federal arrangement of the UK nations to avoid Wales being seen as "some sort of annexe to England".
In Friday's speech, Mr Jones will also say Wales remains "open for business", but will repeat his call for the UK to "retain access" to the EU single market or risk "needless economic harm on our country and our citizens".
Plaid Cymru leader Leanne Wood said keeping "full membership" of the single market, rather than just access to it, was essential for Welsh exports to avoid punitive tariffs.
Welsh Conservative leader Andrew RT Davies accused Mr Jones of an "unforgivable betrayal of the people of Wales" that could "only harm prospects for inward investment".
In one of his strongest attacks on the first minister, Mr Davies said: "There is a time and a place to discuss constitutional issues, but Carwyn Jones is supposed to be in America to sell Wales to the world like never before.
"Instead, in a speech that came straight out of the Nicola Sturgeon playbook, the first minister chose to talk down the economy and to stoke greater uncertainty over the future of the United Kingdom."
Analysis by BBC Wales political editor Nick Servini
On the face of it, this does sound like a speech Scotland's First Minister Nicola Sturgeon would deliver.
As well saying the constitutional make-up of the UK will have to change post-Brexit, Carwyn Jones also says Wales will not give its consent to any deal unless there is access to the European single market.
The problem is that Wales was the only one of the devolved nations to vote to leave, in almost exactly the same way as England.
Mr Jones's challenge will be persuading people in Wales that membership of the single market is important enough to scupper Brexit when many voted to leave, knowing full well that the terms of international trade could change.
The call for a more federal structure is familiar territory for the first minister but he restates it now at a time when there will be presumably far greater priorities for Theresa May's government as it looks to takes Britain out of the EU.