Recent studies have focused on laser-induced gaps in graphene which have been shown to have a topological origin, thereby hosting robust states at the sample edges. While the focus has remainedmainly on these topological chiral edge states, the Floquet bound states around defects lack a detailed study. In this paper we present such a study covering large defects of different shape and also vacancy-like defects and adatoms at the dynamical gap at h Omega/2 (h Omega being the photon energy). Our results, based on analytical calculations as well as numerics for full tight-binding models, show that the bound states are chiral and appear in a number which grows with the defect size. Furthermore, while the bound states exist regardless of the type of the defect's edge termination (zigzag, armchair, mixed), the spectrum is strongly dependent on it. In the case of top adatoms, the bound state quasienergies depend on the adatoms energy. The appearance of such bound states might open the door to the presence of topological effects on the bulk transport properties of dirty graphene.