Most media content consumed today is provided by digital platforms that aggregate input from diverse sources, where access to information is mediated by recommendation algorithms. One principal challenge in this context is dealing with content that is considered harmful. Striking a balance between competing stakeholder interests, rather than block harmful content altogether, one approach is to minimize the exposure to such content that is induced specifically by algorithmic recommendations. Hence, modeling media items and recommendations as a directed graph, we study the problem of reducing the exposure to harmful content via edge rewiring. We formalize this problem using absorbing random walks, and prove that it is NP-hard and NP-hard to approximate to within an additive error, while under realistic assumptions, the greedy method yields a (1-1/e)-approximation. Thus, we introduce Gamine, a fast greedy algorithm that can reduce the exposure to harmful content with or without quality constraints on recommendations. By performing just 100 rewirings on YouTube graphs with several hundred thousand edges, Gamine reduces the initial exposure by 50%, while ensuring that its recommendations are at most 5% less relevant than the original recommendations. Through extensive experiments on synthetic data and real-world data from video recommendation and news feed applications, we confirm the effectiveness, robustness, and efficiency of Gamine in practice.