Studies of dyadic interaction often examine infants’ social exchanges with their caregivers in settings that constrain their physical properties (e.g., infant posture, fixed seating location for infants and adults). Methodological decisions about the physical arrangements of interaction, however, may limit our ability to understand how posture and position shape them. Here we focused on these embodied properties of dyadic interaction in the context of object play. We followed 30 mother–infant dyads across the first year of life (at 3, 6, 9, and 12 months) and observed them during 5 min of play with a standard set of toys. Using an interval‐based coding system, we measured developmental change in infant posture, how mothers and infants positioned themselves relative to one another, and how they populated interaction spaces with objects. Results showed that mother–infant dyads co‐constructed interaction spaces and that the contributions of each partner changed across development. Dyads progressively adopted a broader spatial co‐orientation during play (e.g., positioned at right angles) across the first year. Moreover, advances in infants’ postural skills, particularly increases in the use of independent sitting in real time, uniquely predicted change in dyadic co‐orientation and infants’ actions with objects, independent of age. Taken together, we show that the embodied properties of dyadic object play help determine how interactions are physically organized and unfold, both in real time and across the first year of life.