In-vitro fertilization (IVF) has become standard practice to address infertility, which affects more than one in ten couples in the US. However, current protocols yield relatively low success rates of about 20% per treatment cycle. A critical but complex and time-consuming step is the grading and selection of embryos for implantation. Although incubators with time-lapse microscopy have enabled computational analysis of embryo development, existing automated approaches either require extensive manual annotations or use opaque deep learning models that are hard for clinicians to validate and trust. We present EmbryoProfiler, a visual analytics system collaboratively developed with embryologists, biologists, and machine learning researchers to support clinicians in visually assessing embryo viability from time-lapse microscopy imagery. Our system incorporates a deep learning pipeline that automatically annotates microscopy images and extracts clinically interpretable features relevant for embryo grading. Our contributions include: (1) a semi-automatic, visualization-based workflow that guides clinicians through fertilization assessment, developmental timing evaluation, morphological inspection, and comparative analysis of embryos; (2) innovative interactive visualizations, such as cell-shape plots, designed to facilitate efficient analysis of morphological and developmental characteristics; and (3) an integrated, explainable machine learning classifier offering transparent, clinically-informed embryo viability scoring to predict live birth outcomes. Quantitative evaluation of our classifier and qualitative case studies conducted with practitioners demonstrate that EmbryoProfiler enables clinicians to make better-informed embryo selection decisions, potentially leading to improved clinical outcomes in IVF treatments.