Several systemic diseases, including thrombotic thrombocytopenic purpura, manifest much of their pathology through activation of endothelium and thrombotic occlusion of small blood vessels, often leading to multi-organ failure and death. Modelling these diseases is hampered by the complex three-dimensional architecture and flow patterns of the microvasculature. Here, we employ engineered microvessels of complex geometry to examine the pathological responses to endothelial activation. Our most striking finding is the capacity of endothelial-secreted von Willebrand factor (VWF) to assemble into thick bundles or complex meshes, depending on the vessel geometry and flow characteristics. Assembly is greatest in vessels of diameter ≤300 μm, with high shear stress or strong flow acceleration, and with sharp turns. VWF bundles and webs bind platelets, leukocytes and erythrocytes, obstructing blood flow and sometimes shearing passing erythrocytes. Our findings uncover the biophysical requirements for initiating microvascular thrombosis and suggest mechanisms for the onset and progression of microvascular diseases.