Changes in cell size often accompany multicellular motion in tissue, and cell number density is known to strongly influence collective migration in monolayers. Density fluctuations in other forms of active matter have been explored extensively, but not the potential role of density fluctuations in collective cell migration. Here we investigate collective motion in cell monolayers, focusing on the divergent component of the migration velocity field to probe density fluctuations. We find spatial patterns of diverging and converging cell groups throughout the monolayers, which oscillate in time with a period of approximately 3-4 h. Simultaneous fluorescence measurements of a cytosol dye within the cells show that fluid passes between groups of cells, facilitating these oscillations in cell density. Our findings reveal that cell-cell interactions in monolayers may be mediated by intercellular fluid flow.