The paper considers the method of hierarchical information-extreme machine learning for the system of ophthalmic diagnosis of eye pathology. Since the proposed method is developed within the framework of a functional approach to modeling the cognitive processes of natural intelligence, it, unlike neuro-like structures, acquires the properties of flexibility when retraining a diagnostic system and requires an order of magnitude fewer image samples. In addition, the decision rules based on the results of machine learning within the geometric approach in the form of a binary hierarchical structure of recognition classes ensure their practical invariance to the multidimensionality of both the space of diagnostic features and the alphabet of recognition classes. The modified Kullback-Leibler information measure, which is considered as a function of the accuracy of classification solutions, is chosen as a criterion for optimizing the parameters of the machine learning system for diagnosing eye pathologies. A hierarchical information-extreme machine learning algorithm for an ophthalmic diagnostic system for six eye pathologies was developed and programmatically implemented. Based on the results of functional diagnostics, it has been experimentally proved that the constructed decision rules are error-free according to the training matrices of recognition classes of each level of the constructed binary hierarchical structure.