(1) Background: Hypodontia has a multifactorial aetiology, in which genetic factors are a major component. Associated with this congenital absence, the formed teeth may show differences in size and shape, which may vary with the specific genetic variants and with the location of the missing teeth. The aims of the present study were to investigate a specific variant of MSX1, derive morphometric tooth measurements in a sample of patients with isolated maxillary lateral incisor agenesis and matched controls, and model the findings. (2) Methods: Genotyping of the MSX1 rs8670 genetic variant and morphometric measurements with a 2D image analysis method were performed for 26 hypodontia patients and 26 matched controls. (3) Results: The risk of upper lateral incisor agenesis was 6.9 times higher when the T allele was present. The morphometric parameters showed significant differences between hypodontia patients and controls and between the unilateral and bilateral agenesis cases. The most affected crown dimension in the hypodontia patients was the bucco-lingual dimension. In crown shape there was significant variation the Carabelli trait in upper first molars. (4) Conclusions: The MSX1 rs8670 variant was associated with variations in morphological outcomes. The new findings for compensatory interactions between the maxillary incisors indicate that epigenetic and environmental factors interact with this genetic variant. A single-level directional complex interactive network model incorporates the variations seen in this study.