Large Language Models (LLMs) are increasingly integrated into various medical fields, including mental health support systems. However, there is a gap in research regarding the effectiveness of LLMs in non-English mental health support applications. To address this problem, we present a novel multilingual adaptation of widely-used mental health datasets, translated from English into six languages (Greek, Turkish, French, Portuguese, German, and Finnish). This dataset enables a comprehensive evaluation of LLM performance in detecting mental health conditions and assessing their severity across multiple languages. By experimenting with GPT and Llama, we observe considerable variability in performance across languages, despite being evaluated on the same translated dataset. This inconsistency underscores the complexities inherent in multilingual mental health support, where language-specific nuances and mental health data coverage can affect the accuracy of the models. Through comprehensive error analysis, we emphasize the risks of relying exclusively on large language models (LLMs) in medical settings (e.g., their potential to contribute to misdiagnoses). Moreover, our proposed approach offers significant cost savings for multilingual tasks, presenting a major advantage for broad-scale implementation.