An important question is how growing tissues establish a blood vessel network. Here we study vascular network formation in pancreatic islets, endocrine tissues derived from pancreatic epithelium. We find that depletion of integrin-linked kinase (ILK) in the pancreatic epithelial cells of mice results in glucose intolerance due to a loss of the intra-islet vasculature. In turn, blood vessels accumulate at the islet periphery. Neither alterations in endothelial cell proliferation, apoptosis, morphology, Vegfa expression and VEGF-A secretion nor 'empty sleeves' of vascular basement membrane are found. Instead, biophysical experiments reveal that the biomechanical properties of pancreatic islet cells, such as their actomyosin-mediated cortex tension and adhesive forces to endothelial cells, are significantly changed. These results suggest that a sorting event is driving the segregation of endothelial and epithelial cells and indicate that the epithelial biomechanical properties determine whether the blood vasculature invades or envelops a growing epithelial tissue.