Collective cell migration is an essential process throughout the lives of multicellular organisms, for example in embryonic development, wound healing and tumour metastasis. Substrates or interfaces associated with these processes are typically curved, with radii of curvature comparable to many cell lengths. Using both artificial geometries and lung alveolospheres derived from human induced pluripotent stem cells, here we show that cells sense multicellular-scale curvature and that it plays a role in regulating collective cell migration. As the curvature of a monolayer increases, cells reduce their collectivity and the multicellular flow field becomes more dynamic. Furthermore, hexagonally shaped cells tend to aggregate in solid-like clusters surrounded by non-hexagonal cells that act as a background fluid. We propose that cells naturally form hexagonally organized clusters to minimize free energy, and the size of these clusters is limited by a bending energy penalty. We observe that cluster size grows linearly as sphere radius increases, which further stabilizes the multicellular flow field and increases cell collectivity. As a result, increasing curvature tends to promote the fluidity in multicellular monolayer. Together, these findings highlight the potential for a fundamental role of curvature in regulating both spatial and temporal characteristics of three-dimensional multicellular systems.