Human sleep is one of the essential indicators that gauge the overall health and well-being. Presently, it is common for people to face issues related to sleep. Various biomedical signals including electroencephalogram (EEG), electrooculography (EMG), and electrooculography (EOG) are utilized in the diagnosis and during the treatment of sleep disorder cases. An automatic classification to diagnose sleep problems can help in the analysis of sleep EEG data. In this current study, an effort is made to classify the sleep stages from a single EEG channel (C4-A1) based on K-nearest neighbors (K-NN) with three alternative distance metrics. The Euclidean distance is the most commonly used distance measure in K-NN, and no prior study of sleep EEG data has inspected the classification performance of K-NN with various distance measures. Therefore, this study aimed to investigate whether the distance function affects the performance of K-NN in the classification of sleep data. Euclidean, Manhattan and Chebyshev distance measures were individually tested with K-NN classification, and their performances were compared based on accuracy, sensitivity, specificity, F-measure, Kappa statistic and computation time for both Rechtschaffen & Kales and American Academy of Sleep Medicine standard labelings of the sleep stages. The experimental results show that the Manhattan distance function with K = 5 was the best choice for classification of the sleep stages, achieving 98.46% and 98.77% correct rates for the two labelings with comparatively rapid computations.