The embodied-cognition approach views cognition and language as grounded in daily sensorimotor child-environment interactions. Therefore, the attainment of motor milestones is expected to play a role in cognitive-linguistic development. Early attainment of unsupported sitting and independent walking indeed predict better spatial cognition and language at later ages. However, evidence linking these milestones with the development of "spatial" language and evidence regarding factors that might mediate this relation are scarce. The current study examined whether exploration of spatial-relational object properties (e.g., the possibility of containing or stacking) and exploration of the space through self-locomotion mediate the effect of, respectively, age of sitting and age of walking on spatial cognition and spatial language. Thus, we hypothesized that an earlier age of sitting and walking predicts, respectively, higher levels of spatial-relational object exploration and exploration through self-locomotion, which in turn, predict better spatial cognition and spatial language at later ages. Fifty-nine Dutch children took part in a longitudinal study. A combination of tests, observations, and parental reports was used to measure motor development, exploratory behavior (age 20 months), spatial memory (age 24 months), spatial processing (age 32 months), and spatial language (age 36 months). Results show that attainment of sitting predicted spatial memory and spatial language, but spatial-relational object exploration did not mediate these effects. Attainment of independent walking predicted spatial processing and spatial language, and exploration through self-locomotion (partially) mediated these relations. These findings extend previous work and provide partial support for the hypotheses about the mediating role of exploration.