While large vision-language models (LVLMs) achieve strong performance on multimodal tasks, they frequently generate hallucinations -- unfaithful outputs misaligned with the visual input. To address this issue, we introduce CIPHER (Counterfactual Image Perturbations for Hallucination Extraction and Removal), a training-free method that suppresses vision-induced hallucinations via lightweight feature-level correction. Unlike prior training-free approaches that primarily focus on text-induced hallucinations, CIPHER explicitly targets hallucinations arising from the visual modality. CIPHER operates in two phases. In the offline phase, we construct OHC-25K (Object-Hallucinated Counterfactuals, 25,000 samples), a counterfactual dataset consisting of diffusion-edited images that intentionally contradict the original ground-truth captions. We pair these edited images with the unchanged ground-truth captions and process them through an LVLM to extract hallucination-related representations. Contrasting these representations with those from authentic (image, caption) pairs reveals structured, systematic shifts spanning a low-rank subspace characterizing vision-induced hallucination. In the inference phase, CIPHER suppresses hallucinations by projecting intermediate hidden states away from this subspace. Experiments across multiple benchmarks show that CIPHER significantly reduces hallucination rates while preserving task performance, demonstrating the effectiveness of counterfactual visual perturbations for improving LVLM faithfulness. Code and additional materials are available at https://hamidreza-dastmalchi.github.io/cipher-cvpr2026/.