We predict a magneto-optical Kerr rotation from a magnetized surface in the transverse geometry at normal incidence which is linear in the surface magnetization and is forbidden in the bulk. This surface-induced transverse magneto-optical Kerr effect (SITMOKE) is found to vanish at most bulk-terminated low-index faces of cubic media but is allowed at lower-symmetry planes so that SITMOKE is therefore suitable to study the magnetism of vicinal and reconstructed surfaces. The existence of SITMOKE is demonstrated by detection of an analogous strain-induced effect in a magnetic garnet film with a (210) crystallographic orientation.