Documentation errors increase healthcare costs and cause unnecessary patient deaths. As the standard language for diagnoses and billing, ICD codes serve as the foundation for medical documentation worldwide. Despite the prevalence of electronic medical records, hospitals still witness high levels of ICD miscoding. In this paper, we propose to automatically document ICD codes with far-field speech recognition. Far-field speech occurs when the microphone is located several meters from the source, as is common with smart homes and security systems. Our method combines acoustic signal processing with recurrent neural networks to recognize and document ICD codes in real time. To evaluate our model, we collected a far-field speech dataset of ICD-10 codes and found our model to achieve 87% accuracy with a BLEU score of 85%. By sampling from an unsupervised medical language model, our method is able to outperform existing methods. Overall, this work shows the potential of automatic speech recognition to provide efficient, accurate, and cost-effective healthcare documentation.