Melanoma is a kind of skin cancer caused by the irregular development of pigment-producing cells. Since melanoma detection efficiency is limited to different factors such as poor contrast among lesions and nearby skin regions, and visual resemblance among melanoma and non-melanoma lesions, intelligent computer-aided diagnosis (CAD) models are essential. Recently, computational intelligence (CI) and deep learning (DL) techniques are utilized for effective decision-making in the biomedical field. In addition, the fast-growing advancements in computer-aided surgeries and recent progress in molecular, cellular, and tissue engineering research have made CI an inevitable part of biomedical applications. In this view, the research work here develops a novel computational intelligence-based melanoma detection and classification technique using dermoscopic images (CIMDC-DIs). The proposed CIMDC-DI model encompasses different subprocesses. Primarily, bilateral filtering with fuzzy k-means (FKM) clustering-based image segmentation is applied as a preprocessing step. Besides, NasNet-based feature extractor with stochastic gradient descent is applied for feature extraction. Finally, the manta ray foraging optimization (MRFO) algorithm with a cascaded neural network (CNN) is exploited for the classification process. To ensure the potential efficiency of the CIMDC-DI technique, we conducted a wide-ranging simulation analysis, and the results reported its effectiveness over the existing recent algorithms with the maximum accuracy of 97.50%.