Deep learning can be used effectively to predict participants' age from brain magnetic resonance imaging (MRI) data, and a growing body of evidence suggests that the difference between predicted and chronological age—referred to as brain-predicted age difference (brain-PAD)—is related to various neurological and neuropsychiatric disease states. A crucial aspect of the applicability of brain-PAD as a biomarker of individual brain health is whether and how brain-predicted age is affected by MR image artifacts commonly encountered in clinical settings. To investigate this issue, we trained and validated two different 3D convolutional neural network architectures (CNNs) from scratch and tested the models on a separate dataset consisting of motion-free and motion-corrupted T1-weighted MRI scans from the same participants, the quality of which were rated by neuroradiologists from a clinical diagnostic point of view. Our results revealed a systematic increase in brain-PAD with worsening image quality for both models. This effect was also observed for images that were deemed usable from a clinical perspective, with brains appearing older in medium than in good quality images. These findings were also supported by significant associations found between the brain-PAD and standard image quality metrics indicating larger brain-PAD for lower-quality images. Our results demonstrate a spurious effect of advanced brain aging as a result of head motion and underline the importance of controlling for image quality when using brain-predicted age based on structural neuroimaging data as a proxy measure for brain health.