The selection of sperm cells possessing normal morphology and motility is crucial for many assisted reproductive technologies (ART) as sperm quality directly affects the probability of inducing healthy pregnancy. We present a novel platform for real-time quantitative analysis and selection of individual sperm cells without staining. Towards this end, we combined interferometric phase microscopy (IPM), for stain-free sperm imaging and real-time automated classification, with a disposable microfluidic device, for sperm selection and enrichment. Over 1,400 human sperm cells from 8 donors were imaged using IPM, and an algorithm was designed to digitally isolate sperm cell heads from the quantitative phase maps while taking into consideration both the cell 3D morphology and contents, as well as acquire features describing sperm head morphology. A subset of these features was used to train a support vector machine (SVM) classifier to automatically classify sperm of good and bad morphology. The SVM achieves an area under the receiver operating characteristic curve of 88.59% and an area under the precision-recall curve of 88.67%, as well as precisions of 90% or higher. The microfluidic device was then manufactured and tested. Upon testing the device, we obtained successful selection of sperm cells with a selectivity of 89.5 ± 3.5%, with no negative-decision sperm cells being inadvertently selected. We believe that the presented integrated approach has the potential to dramatically change the way sperm cells are selected for ICSI and other ART procedures, making the selection process more objective, quantitative and automatic, and thereby increasing success rates.