Magnetic resonance imaging (MRI) is invaluable for the detailed visualization of soft tissues. However, its susceptibility to motion artifacts presents a challenge in ophthalmology due to the continuous eye movement. A recently developed technique effectively resolves eye motion in MRI, but it strongly relies on an eye tracker (ET), which, being a resource-intensive system, limits its broader adoption. The present work introduces a novel approach that, based on machine learning techniques, enables automated identification of eye motion in raw MRI data collected using a fast-sampling acquisition strategy. Such MRI data were acquired from nine healthy subjects while visual stimuli directed their gaze. A synchronized ET signal was also recorded to label the data. A broad spectrum of features representing the raw MRI acquisitions were extracted, and the classification models were built based on the most discriminative ones. Motion identification was primarily driven by phase-related features, while the models achieved accuracy and recall values exceeding 98%. This study represents an important first step towards obtaining a high-quality MRI of the eye without depending on supplementary hardware.