A multicellular organism is not a monolayer of cells in a flask; it is a complex, spatially structured environment, offering both challenges and opportunities for viruses to thrive. Whereas virus infection dynamics at the host and within-cell levels have been documented, the intermediate between-cell level remains poorly understood. Here, we used flow cytometry to measure the infection status of thousands of individual cells in virus-infected plants. This approach allowed us to determine accurately the number of cells infected by two virus variants in the same host, over space and time as the virus colonizes the host. We found a low overall frequency of cellular infection (<0.3), and few cells were coinfected by both virus variants (<0.1). We then estimated the cellular contagion rate (R), the number of secondary infections per infected cell per day. R ranged from 2.43 to values not significantly different from zero, and generally decreased over time. Estimates of the cellular multiplicity of infection (MOI), the number of virions infecting a cell, were low (<1.5). Variance of virus-genotype frequencies increased strongly from leaf to cell levels, in agreement with a low MOI. Finally, there were leaf-dependent differences in the ease with which a leaf could be colonized, and the number of virions effectively colonizing a leaf. The modeling of infection patterns suggests that the aggregation of virus-infected cells plays a key role in limiting spread; matching the observation that cell-to-cell movement of plant viruses can result in patches of infection. Our results show that virus expansion at the between-cell level is restricted, probably due to the host environment and virus infection itself.