Sperm morphology, as an indicator of fertility, is a critical tool in semen analysis. In this study, a smartphone-based hybrid system that fully automates the sperm morphological analysis is introduced with the aim of eliminating unwanted human factors. Proposed hybrid system consists of two progressive steps: automatic segmentation of possible sperm shapes and classification of normal/ab-normal sperms. In the segmentation step, clustering techniques with/without group sparsity approach were tested to extract region of interests from the images. Subsequently, a novel publicly available morphological sperm image data set, whose labels were identified by experts as non-sperm, normal and abnormal sperm, was created as the ground truths of classification step. In the classification step, conventional and ensemble machine learning methods were applied to domain-specific features that were extracted by using wavelet transform and descriptors. Additionally, as an alternative to conventional features, three deep neural network architectures, which can extract high-level features from raw images after using statistical learning, were employed to increase the proposed method's performance. The results show that, for the conventional features, the highest classification accuracies were achieved as 80.5% and 83.8% by using the wavelet- and descriptor-based features that were fed to the Support Vector Machines respectively. On the other hand, the Mobile-Net, which is a very convenient network for smartphones, achieved 87% accuracy. In the light of obtained results, it is seen that a fully automatic hybrid system, which uses the group sparsity to enhance segmentation performance and the Mobile-Net to obtain high-level robust features, can be an effective mobile solution for the sperm morphology analysis problem.