The atomic and electronic structure of intrinsic defects in a WSe_{2} monolayer grown on graphite was revealed by low temperature scanning tunneling microscopy and spectroscopy. Instead of chalcogen vacancies that prevail in other transition metal dichalcogenide materials, intrinsic defects in WSe_{2} arise surprisingly from single tungsten vacancies, leading to the hole (p-type) doping. Furthermore, we found these defects to dominate the excitonic emission of the WSe_{2} monolayer at low temperature. Our work provided the first atomic-scale understanding of defect excitons and paved the way toward deciphering the defect structure of single quantum emitters previously discovered in the WSe_{2} monolayer.