Regarding software engineering (SE) tasks, Large language models (LLMs) have the capability of zero-shot learning, which does not require training or fine-tuning, unlike pre-trained models (PTMs). However, LLMs are primarily designed for natural language output, and cannot directly produce intermediate embeddings from source code. They also face some challenges, for example, the restricted context length may prevent them from handling larger inputs, limiting their applicability to many SE tasks; while hallucinations may occur when LLMs are applied to complex downstream tasks. Motivated by the above facts, we propose zsLLMCode, a novel approach that generates functional code embeddings using LLMs. Our approach utilizes LLMs to convert source code into concise summaries through zero-shot learning, which is then transformed into functional code embeddings using specialized embedding models. This unsupervised approach eliminates the need for training and addresses the issue of hallucinations encountered with LLMs. To the best of our knowledge, this is the first approach that combines LLMs and embedding models to generate code embeddings. We conducted experiments to evaluate the performance of our approach. The results demonstrate the effectiveness and superiority of our approach over state-of-the-art unsupervised methods.