The automatic diagnosis of melanoma is usually affected by the noise that is often included in an image, during the acquisition stage or by superficial factors such as hair. Specifically, hair on the surface of a lesion can cause enough distortion, resulting in an erroneous diagnosis of the region of interest. To solve this issue, several techniques have been presented to detect hair on the surface of a dermoscopy image and substitute a surface approximation for these regions. Nonetheless, the existing methods are prone to false detections or reconstructions that are not uniform, demand high computing resources and modify the textures of important characteristics. Therefore, we proposed a method that detects the hairs by means of a convolution of the image with a kernel belonging to the first derivative of the Gaussian function and replaces the hairs using a multiscale morphological reconstruction. In addition, we integrated a refining stage that contributes to maintaining the quality of the patterns on the lesion. We used 36 dermoscopy images in the evaluation, which included a total of 586 hairs that were automatically detected with the proposed process and validated with their respective manual segmentations. Our results showed sensitivity and specificity performance measurements of 94.14% and 99.89%, respective.