Skeletal muscle cells contain hundreds of myonuclei within a shared cytoplasm, presenting unique challenges for regulating gene expression. Certain transcriptional programs (e.g., postsynaptic machinery) are segregated to specialized domains, while others (e.g., contractile proteins) do not show spatial confinement. Furthermore, local stimuli, such as denervation, can induce transcriptional responses that are propagated along the muscle cells. Regulated transport of nuclear proteins (e.g., transcription factors) between myonuclei represents a potential mechanism for coordinating gene expression. However, the principles underlying the transport of nuclear proteins within multinucleated cells remain poorly defined. Here we used a mosaic transfection model to create myotubes that contained exactly one myonucleus expressing a fluorescent nuclear reporter and monitored its distribution among all myonuclei. We found that the transport properties of these model nuclear proteins in myotubes depended on molecular weight and nuclear import rate, as well as on myotube width. Interestingly, muscle hypertrophy increased the transport of high molecular weight nuclear proteins, while atrophy restricted the transport of smaller nuclear proteins. We have developed a mathematical model of nuclear protein transport within a myotube that recapitulates the results of our in vitro experiments. To test the relevance to nuclear proteins expressed in skeletal muscle, we studied the transport of two transcription factors—aryl hydrocarbon receptor nuclear translocator and sine oculis homeobox 1—and found that their distributions were similar to the reporter proteins with corresponding molecular weights. Together, these results define a set of variables that can be used to predict the spatial distributions of nuclear proteins within a myotube.