We present an ab initio study of the influence of hydrogen impurities (atoms and molecules) on the atomic structure and electronic properties of Pd nanowires and atomic-size nanocontacts. Various atomic positions for hydrogen adsorption within palladium structures are considered. It is found that adsorbed hydrogen can penetrate into the atomic structure of Pd nanocontacts and nanowires and by that increase their stability close to and beyond their breaking points. The interaction between hydrogen and palladium atoms alters the interatomic bonding and hybridization of electronic states of palladium atoms. The interaction of palladium with hydrogen leads to the suppression of magnetic properties of Pd nanowires and nanocontacts. Additionally, the possibility of dissociation of molecular hydrogen at palladium nanocontacts is discussed, which is an important issue for catalytic applications.