In the present study, the recovery of valuable metals from a Panasonic Prismatic Module 6.5 Ah NiMH 7.2 V plastic casing hybrid electric vehicle (HEV) battery has been investigated, processing the anode and cathode electrodes separately. The study focuses on the recovery of the most valuable compounds, i.e., nickel, cobalt and rare earth elements (REE). Most of the REE (La, Ce, Nd, Pr and Y) were found in the anode active material (33% by mass), whereas only a small amount of Y was found in the cathode material. The electrodes were leached in sulfuric acid and in hydrochloric acid, respectively, under different conditions. The results indicated that the dissolution kinetics of nickel could be slow as a result of slow dissolution kinetics of nickel oxide. At leaching in sulfuric acid, light rare earths were found to reprecipitate increasingly with increasing temperature and sulfuric acid concentration. Following the leaching, the separation of REE from the sulfuric acid leach liquor by precipitation as NaREE (SO4)2·H2O and from the hydrochloric acid leach solution as REE2(C2O4)3·xH2O were investigated. By adding sodium ions, the REE could be precipitated as NaREE (SO4)2·H2O with little loss of Co and Ni. By using a stoichiometric oxalic acid excess of 300%, the REE could be precipitated as oxalates while avoiding nickel and cobalt co-precipitation. By using nanofiltration it was possible to recover hydrochloric acid after leaching the anode material.