An online social network can be used for the diffusion of malicious information like derogatory rumors, disinformation, hate speech, revenge pornography, etc. This motivates the study of influence minimization that aim to prevent the spread of malicious information. Unlike previous influence minimization work, this study considers the influence minimization in relation to a particular group of social network users, called targeted influence minimization. Thus, the objective is to protect a set of users, called target nodes, from malicious information originating from another set of users, called active nodes. This study also addresses two fundamental, but largely ignored, issues in different influence minimization problems: (i) the impact of a budget on the solution; (ii) robust sampling. To this end, two scenarios are investigated, namely unconstrained and constrained budget. Given an unconstrained budget, we provide an optimal solution; Given a constrained budget, we show the problem is NP-hard and develop a greedy algorithm with an (1−1e)-approximation. More importantly, in order to solve the influence minimization problem in large, real-world social networks, we propose a robust sampling-based solution with a desirable theoretic bound. Extensive experiments using real social network datasets offer insight into the effectiveness and efficiency of the proposed solutions.