Contents of platinum group elements (PGE—Os, Ir, Ru, Rh, Pt, and Pd) and rhenium in basalts of different geochemical types from the ophiolite complex of the Kamchatsky Mys Peninsula have been determined by the isotope dilution–mass spectrometry method. The total contents of PGE in different basalts are commensurate (1.4–3.6 ppb), but the element ratios vary considerably. A specific feature of the rocks is the low degree of PGE fractionation (Pd/Ir = 0.9–6.6, Pt/Pd = 1.0–7.3), which makes them similar to the Hawaiian tholeiitic basalts and picrites. The most fractionated PGE pattern is observed for alkali basalt (Pd/Ir = 6.6), and the least fractionated one, for E-MORB (Pd/Ir = 1.7). The similarity of the PGE patterns of basalts of different geochemical types suggests their similar mantle sources. We propose a model explaining the geochemical features of the basalts of the Kamchatsky Mys ophiolite complex by an impurity of the Earth’s core material in the plume source. The Ir/Pd–Ru/Pd and Pd/10–Ir–Ru discrimination diagrams can be used to identify enriched (plume) basalts based on their PGE content.