We study exact impulsive gravitational waves propagating in anti-de Sitter spacetime in the context of the ghost-free infinite derivative gravity. We show that the source-free theory does not admit any anti-de Sitter wave solutions other than that of Einstein's general relativity. The situation is significantly different in the presence of sources. We construct impulsive-wave solutions of the infinite derivative gravity generated by massless particles and linear sources in four and three dimensions. The singularities corresponding to distributional curvature at the locations of the sources get smeared by the nonlocalities. The obtained solutions are regular everywhere. They reduce to the corresponding solutions of general relativity in the infrared regime and in the local limit.
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