We introduce MENAValues, a novel benchmark designed to evaluate the cultural alignment and multilingual biases of large language models (LLMs) with respect to the beliefs and values of the Middle East and North Africa (MENA) region, an underrepresented area in current AI evaluation efforts. Drawing from large-scale, authoritative human surveys, we curate a structured dataset that captures the sociocultural landscape of MENA with population-level response distributions from 16 countries. To probe LLM behavior, we evaluate diverse models across multiple conditions formed by crossing three perspective framings (neutral, personalized, and third-person/cultural observer) with two language modes (English and localized native languages: Arabic, Persian, Turkish). Our analysis reveals three critical phenomena: "Cross-Lingual Value Shifts" where identical questions yield drastically different responses based on language, "Reasoning-Induced Degradation" where prompting models to explain their reasoning worsens cultural alignment, and "Logit Leakage" where models refuse sensitive questions while internal probabilities reveal strong hidden preferences. We further demonstrate that models collapse into simplistic linguistic categories when operating in native languages, treating diverse nations as monolithic entities. MENAValues offers a scalable framework for diagnosing cultural misalignment, providing both empirical insights and methodological tools for developing more culturally inclusive AI.