Spatial skills predict important life outcomes, such as mathematical achievement or entrance into Science, Technology, Engineering, and Mathematics (STEM) disciplines. Children significantly vary in their spatial performance even before they enter formal schooling. One correlate of children’s spatial performance is the spatial language they produce and hear from others, such as their parents. Because the emphasis has been on spatial language, less is known about the role of hand gestures in children’s spatial development. Some children are more likely to fall behind in their spatial skills than others. Children born premature (gestational age <37 weeks) constitute such a risk group. Here, we compared performance of term and preterm-born children on two non-verbal spatial tasks—mental transformation and block design. We also examined relations of children’s performance on these tasks to parental spatial language and gesture input and their own production of spatial language and gesture during an independent puzzle play interaction. We found that while term and preterm-born children (n = 40) as a group did not differ in the mental transformation or block design performance, children varied widely in their performance within each group. The variability in mental transformation scores was predicted by both a subset of spatial words (what aspects of spatial information) and all spatial gestures children produced. Children’s spatial language and gesture were in turn related to their parents’ spatial language and gesture. Parental spatial language and gesture had an indirect relation on children’s mental transformation, but not block design, scores via children’s spatial language, and gesture use. Overall, results highlight the unique contributions of speech and gesture in communicating spatial information and predicting children’s spatial performance.