Metal halide perovskite solar cells hold great promise as an efficient and cost-effective photovoltaic technology. However, carrier recombination at their contacts impedes progress toward this goal. In this study, considering the archetypical MAPbI3 perovskite and Au as a model electrode, we employ first-principles calculations to show how the mere presence of a metal near the perovskite induces in-gap states that may impair electronically this contact because of carrier recombination and Fermi level pinning. The states are not associated with any defect. We then investigate the suppression of the contact-induced gap states by introducing various passivation molecules to displace the metal from the perovskite surface. Our results highlight from a fundamental perspective the importance of contact displacement and passivation for efficient perovskite solar cells, thereby elucidating further the role of thin molecular interlayers in experimental devices. The elimination of contact-induced gap states can greatly aid perovskite solar cells in fulfilling their promise as a future mainstream source of renewable electricity.