Medical data hiding is used to hide patient information inside medical images to protect patient privacy. Patient information in the image should be protected when sending medical images to other specialists or hospitals over the communication network. However, the images are exposed to various unwanted disruptive signals in the communication channel. One of these signals is salt and pepper noise. A pixel exposed to salt and pepper noise becomes completely black or completely white. In pixel-based data hiding methods, it is not possible to extract the secret message in the pixel exposed to this kind of noise. While current data hiding methods are good for many disruptive effects, they are weak against salt and pepper noise. For this reason, the proposed study especially focuses on the accurate extraction of patient information in the salt and pepper noisy medical images. This study was proposed for the most accurate extraction of secret message despite salt and pepper noise, by use of a Reed Solomon error control coding-based data hiding method. The most important feature of Reed Solomon codes is that they can correct errors in non-binary (decimal) numbers directly. Therefore, the Reed Solomon coding-based data hiding method that proposed in this study increases the resistance against salt and pepper noise. Experimental studies show that secret data is accurately extracted from stego images with various densities of salt and pepper noise. Stego medical images created by the proposed method have superior quality values compared to similar literature studies. Additionally, compared to similar methods, the secret message is extracted from the noisy stego image with higher accuracy.