SPG4 is an autosomal dominant pure form of hereditary spastic paraplegia (HSP) caused by mutations in the SPAST gene. HSP is considered an upper motor neuron disorder characterized by progressive spasticity and weakness of the lower limbs caused by degeneration of the corticospinal tract. In other neurodegenerative motor disorders, the thalamus and basal ganglia are affected, with a considerable impact on disease progression. However, only a few works have studied these brain structures in HSP, mainly in complex forms of this disease. Our research aims to detect potential alterations in the volume and shape of the thalamus and various basal ganglia structures by comparing 12 patients with pure HSP and 18 healthy controls. We used two neuroimaging procedures: automated segmentation of the subcortical structures (thalamus, hippocampus, caudate nucleus, globus pallidus, and putamen) in native space and shape analysis of the structures. We found a significant reduction in thalamic volume bilaterally, as well as an inward deformation, mainly in the sensory-motor thalamic regions in patients with pure HSP and a mutation in SPG4. We also observed a significant negative correlation between the shape of the thalamus and clinical scores (the Spastic Paraplegia Rating Scale score and disease duration). Moreover, we found a 'Group × Age' interaction that was closely related to the severity of the disease. No differences in volume or in shape were found in the remaining subcortical structures studied. Our results suggest that changes in structure of the thalamus could be an imaging biomarker of disease progression in pHSP.