Alterations in brain structures, including progressive neurodegeneration, are a hallmark in patients with Alzheimer’s disease (AD). However, pathological mechanisms, such as the accumulation of amyloid and the proliferation of tau, are thought to begin years, even decades, before the initial clinical manifestations of AD. In this study, we compare the brain anatomy of amnestic mild cognitive impairment patients (aMCI, n = 16) to healthy subjects (CS, n = 22) using cortical thickness, subcortical volume, and shape analysis, which we believe to be complimentary to volumetric measures. We were able to replicate “classical” cortical thickness alterations in aMCI in the hippocampus, amygdala, putamen, insula, and inferior temporal regions. Additionally, aMCI showed significant thalamic and striatal shape differences. We observed higher global amyloid deposition in aMCI, a significant correlation between striatal displacement and global amyloid, and an inverse correlation between executive function and right-hemispheric thalamic displacement. In contrast, no volumetric differences were detected in thalamic, striatal, and hippocampal regions. Our results provide new evidence for early subcortical neuroanatomical changes in patients with aMCI, which are linked to cognitive abilities and amyloid deposition. Hence, shape analysis may aid in the identification of structural biomarkers for identifying individuals at highest risk of conversion to AD.