Collective motion is observed in swarms of swimmers of various sizes, ranging from self-propelled nanoparticles to fish. The mechanisms that govern interactions among individuals are debated, and vary from one species to another. Although the interactions among relatively large animals, such as fish, are controlled by their nervous systems, the interactions among microorganisms, which lack nervous systems, are controlled through physical and chemical pathways. Little is known, however, regarding the mechanism of collective movements in microscopic organisms with nervous systems. To attempt to remedy this, we studied collective swimming behavior in the nematode Caenorhabditis elegans, a microorganism with a compact nervous system. We evaluated the contributions of hydrodynamic forces, contact forces, and mechanosensory input to the interactions among individuals. We devised an experiment to examine pair interactions as a function of the distance between the animals and observed that gait synchronization occurred only when the animals were in close proximity, independent of genes required for mechanosensation. Our measurements and simulations indicate that steric hindrance is the dominant factor responsible for motion synchronization in C. elegans, and that hydrodynamic interactions and genotype do not play a significant role. We infer that a similar mechanism may apply to other microscopic swimming organisms and self-propelled particles.