In its flagship economic survey of the world economy, the IMF acknowledged that there were fundamental "flaws" in the design of the single currency and said that one prospective "tail risk" is a "disorderly default and exit by a euro area member".
It is the first time the IMF has openly contemplated such an outcome.
Its previous forecasts disregarded such a scenario, and its managing director, Christine Lagarde, said earlier this month that it had no agenda to see the euro collapse.
The announcement comes amid growing consternation about the plight of Spain, which has suffered an exodus of bank deposits and is struggling to raise money at reasonable rates.
Many now believe that Spain could follow Greece, Portugal and Ireland in having an emergency bail-out.
The IMF said it was impossible to quantify the impact of a country defaulting or exiting the currency union.
But in its World Economic Outlook, it added: "If such an event occurs, it is possible that other euro area economies perceived to have similar risk characteristics would come under severe pressure as well, with a full-blown panic in financial markets and depositor flight from several banking systems.
"Under these circumstances, a breakup of the euro area could not be ruled out.
"The financial and real spillovers to other regions, especially emerging Europe, would likely be very large.
"This could cause major political shocks that could aggravate economic stress to levels well above those after the Lehman collapse."
However, the IMF's working assumption is that "policymakers succeed in containing the sovereign crisis through continued crisis management and further advancing measures toward its resolution".
Nonetheless, it raised its forecast for overall world economic growth this year by 0.2% points to 3.5%.
It also increased its economic growth forecast for the UK this year from 0.6% to 0.8%, the first such increase in recent years, which is likely to reinforce Chancellor George Osborne's insistence that he is following the right path.
However, it is the IMF's warning over Europe which is likely to disturb policymakers most profoundly.
It cut its economic growth forecast for Spain this year from -1.6% to -1.8%, which is lower than Madrid's official forecast and makes it harder to meet its deficit reduction plans.
That comes with Spain facing government borrowing costs of more than 6%, a sign that investors are fearful of buying the country's debt.
And in a further blow, the country has become embroiled in a row with Argentina, which is set to nationalise its oil company YPF, the majority stake of which is owned by Spanish oil group Repsol.