Fetal MRI plays a critical role in diagnosing brain abnormalities but routinely suffers from artifacts resulting in nondiagnostic images. We aim to automatically identify nondiagnostic images during acquisition so they can be immediately flagged for reacquisition. As a first step, we trained a neural network to classify T2-weighted single-shot fast spin-echo (HASTE) images as diagnostic or nondiagnostic. With novel data, the average Area Under Receiver Operator Characteristic Curve was 0.84 (σ = 0.04). The neural network learned relevant criteria, identifying high contrast boundaries between areas like cerebral spinal fluid and cortical plate as relevant to determining image quality.