The ability to perform dynamic imaging of time-varying physiological processes in small animal models is critically needed to understand the progression of human diseases and develop new therapies. Photoacoustic computed tomography (PACT) has been recognized as a promising tool for small animal imaging because of its relatively low expense, high resolution, and good signal-to-noise ratio. By exploiting the optical absorption of hemoglobin or exogenous contrast agents, dynamic PACT holds excellent potential for measuring important time-varying biomarkers like tumor vascular perfusion. Nonetheless, current dynamic PACT technologies possess several limitations. Most three-dimensional (3D) PACT imagers employ a tomographic measurement process in which a gantry containing acoustic transducers is rotated about the animal. Such a rotating gantry is advantageous for limiting the cost of the system due to the decreased number of acoustic transducers and associated electronics and for enabling convenient delivery of the light to the object. However, this presents significant challenges for dynamic image reconstruction because only a few tomographic views are available to reconstruct each temporal frame. This work presents an efficient and accurate dynamic image reconstruction method that can be deployed with widely available 3D imagers using rotating gantries. In particular, a low-rank matrix estimation-based spatiotemporal image reconstruction (LRME-STIR) algorithm is proposed. In a stylized virtual dynamic contrast-enhanced imaging study, the proposed LRME-STIR algorithm is shown to accurately recover a well-characterized dynamic numerical murine phantom in which tumor vascular perfusion and breathing motion are modeled.