The Russian invasion of Ukraine is a major threat to the global food system, which requires international cooperation and leadership to avert a crisis. To better understand this threat, we explore multiple scenarios for global annual wheat prices and country supplies. We find that prices could spike by up to 65%, exceeding the price spikes of the two recent world food price crises in 2007/08 and 2010/11 if the war escalates any further and national policymakers react uncoordinatedly and unilaterally. Timely and concerted action by key food-producing countries and international institutions is needed to address both the urgent humanitarian needs and the rapid, short-term structural changes in global supply and trade. Additionally, the developing crisis highlights the importance of rapid and integrated analyses of systemic risks from global to regional scales together with robust scenario analyses that include policy and business responses and interventions.