System prompts that include detailed instructions to describe the task performed by the underlying large language model (LLM) can easily transform foundation models into tools and services with minimal overhead. Because of their crucial impact on the utility, they are often considered intellectual property, similar to the code of a software product. However, extracting system prompts is easily possible by using prompt injection. As of today, there is no effective countermeasure to prevent the stealing of system prompts and all safeguarding efforts could be evaded with carefully crafted prompt injections that bypass all protection mechanisms. In this work, we propose an alternative to conventional system prompts. We introduce prompt obfuscation to prevent the extraction of the system prompt while maintaining the utility of the system itself with only little overhead. The core idea is to find a representation of the original system prompt that leads to the same functionality, while the obfuscated system prompt does not contain any information that allows conclusions to be drawn about the original system prompt. We implement an optimization-based method to find an obfuscated prompt representation while maintaining the functionality. To evaluate our approach, we investigate eight different metrics to compare the performance of a system using the original and the obfuscated system prompts, and we show that the obfuscated version is constantly on par with the original one. We further perform three different deobfuscation attacks and show that with access to the obfuscated prompt and the LLM itself, we are not able to consistently extract meaningful information. Overall, we showed that prompt obfuscation can be an effective method to protect intellectual property while maintaining the same utility as the original system prompt.