Learning the names of geometric shapes is at the intersection of early spatial, mathematical, and language skills, all important for school-readiness and predictors of later abilities in science, technology, engineering, and mathematics (STEM). We investigated whether socioeconomic status (SES) influenced children’s processing of shape names and whether differences in processing were predictive of later spatial skills. Three-year-olds (N = 79) with mothers of varying education levels participated in an eye-tracking task that required them to look at named shapes. Lower SES children took longer to fixate target shapes and spent less time looking at them than higher SES children. Gaze variables measured at age 3 were predictive of spatial skills measured at age 5 even though the spatial measures did not require shape-related vocabulary. Early efficiency in the processing of shape names may contribute to the development of a foundation for spatial learning in the preschool years.