Cilia-generated fluid flow in an ‘organ of asymmetry’ is critical for establishing the left-right body axis in several vertebrate embryos. However, the cell biology underlying how motile cilia produce coordinated flow and asymmetric signals is not well defined. In the zebrafish organ of asymmetry—called Kupffer’s vesicle (KV)—ciliated cells are asymmetrically positioned along the anterior-posterior axis such that more cilia are placed in the anterior region. We previously demonstrated that Rho kinase 2b (Rock2b) is required for anteroposterior asymmetry and fluid flow in KV, but it remained unclear how the distribution of ciliated cells becomes asymmetric during KV development. Here, we identify a morphogenetic process we refer to as ‘KV remodeling’ that transforms initial symmetry in KV architecture into anteroposterior asymmetry. Live imaging of KV cells revealed region-specific cell shape changes that mediate tight packing of ciliated cells into the anterior pole. Mathematical modeling indicated that different interfacial tensions in anterior and posterior KV cells are involved in KV remodeling. Interfering with non-muscle myosin II (referred to as Myosin II) activity, which modulates cellular interfacial tensions and is regulated by Rock proteins, disrupted KV cell shape changes and the anteroposterior distribution of KV cilia. Similar defects were observed in Rock2b depleted embryos. Furthermore, inhibiting Myosin II at specific stages of KV development perturbed asymmetric flow and left-right asymmetry. These results indicate that regional cell shape changes control the development of anteroposterior asymmetry in KV, which is necessary to generate coordinated asymmetric fluid flow and left-right patterning of the embryo.