Arsenic vacancies in LaFeAsO-derived superconductors are nominally non-magnetic defects. However, we find from a microscopic theory in terms of an appropriately modified Anderson-Wolff model that in their vicinity local magnetic moments form. They can arise because removing an arsenic atom breaks four strong, covalent bonds with the neighboring iron atoms. The moments emerging around an arsenic vacancy orient ferromagnetically and cause a substantial enhancement of the paramagnetic susceptibility in both the normal and superconducting state. The qualitative model description is supported by first principles band structure calculations of the As-vacancy related defect spectrum within a larger supercell.