Anomalies in motor function and social communication skills constitute early signs of autism spectrum disorder (ASD). In recent years, researchers have paid attention to the possibility of the quantitatively evaluating infants’ social communication skills based on their eye movement. In this paper, we attempt to evaluate ASD risk using infants’ eye movement data by examining the relationship between eye movement patterns at 4, 10, and 18 months of age and ASD risk as assessed by caregivers using a checklist at 18 months of age. A total of 18 eye movement indices were calculated from eye movement data measured by an optical eye tracker. The results revealed an association between ASD risk and eye movement indices. The indices included those related to a preference for social information at 4 months of age, those related to visual exploration of images at 10 months of age, and those indices related to both preference and visual exploration at 18 months of age. These results indicate that eye movement analysis may potentially serve as a means for early screening of ASD risk.