Machine unlearning (MU) removes specific data points or concepts from deep learning models to enhance privacy and prevent sensitive content generation. Adversarial prompts can exploit unlearned models to generate content containing removed concepts, posing a significant security risk. However, existing adversarial attack methods still face challenges in generating content that aligns with an attacker's intent while incurring high computational costs to identify successful prompts. To address these challenges, we propose ZIUM, a Zero-shot Intent-aware adversarial attack on Unlearned Models, which enables the flexible customization of target attack images to reflect an attacker's intent. Additionally, ZIUM supports zero-shot adversarial attacks without requiring further optimization for previously attacked unlearned concepts. The evaluation across various MU scenarios demonstrated ZIUM's effectiveness in successfully customizing content based on user-intent prompts while achieving a superior attack success rate compared to existing methods. Moreover, its zero-shot adversarial attack significantly reduces the attack time for previously attacked unlearned concepts.