Despite remarkable advancements in recent voice conversion (VC) systems, enhancing speaker similarity in zero-shot scenarios remains challenging. This challenge arises from the difficulty of generalizing and adapting speaker characteristics in speech within zero-shot environments, which is further complicated by mismatch between the training and inference processes. To address these challenges, we propose VoicePrompter, a robust zero-shot VC model that leverages in-context learning with voice prompts. VoicePrompter is composed of (1) a factorization method that disentangles speech components and (2) a DiT-based conditional flow matching (CFM) decoder that conditions on these factorized features and voice prompts. Additionally, (3) latent mixup is used to enhance in-context learning by combining various speaker features. This approach improves speaker similarity and naturalness in zero-shot VC by applying mixup to latent representations. Experimental results demonstrate that VoicePrompter outperforms existing zero-shot VC systems in terms of speaker similarity, speech intelligibility, and audio quality. Our demo is available at \url{https://hayeong0.github.io/VoicePrompter-demo/}.