Interhemispheric communication may be constrained as brain size increases because of transmission delays in action potentials over the length of axons. Although one might expect larger brains to have progressively thicker axons to compensate, spatial packing is a limiting factor. Axon size distributions within the primate corpus callosum (CC) may provide insights into how these demands affect conduction velocity. We used electron microscopy to explore phylogenetic variation in myelinated axon density and diameter of the CC from 14 different anthropoid primate species, including humans. The majority of axons were less than 1 µm in diameter across all species, indicating that conduction velocity for most interhemispheric communication is relatively constant regardless of brain size. The largest axons within the upper 95th percentile scaled with a progressively higher exponent than the median axons towards the posterior region of the CC. While brain mass among the primates in our analysis varied by 97-fold, estimates of the fastest cross-brain conduction times, as conveyed by axons at the 95th percentile, varied within a relatively narrow range between 3 and 9 ms across species, whereas cross-brain conduction times for the median axon diameters differed more substantially between 11 and 38 ms. Nonetheless, for both size classes of axons, an increase in diameter does not entirely compensate for the delay in interhemispheric transmission time that accompanies larger brain size. Such biophysical constraints on the processing speed of axons conveyed by the CC may play an important role in the evolution of hemispheric asymmetry.