Large mammalian herbivores exert strong top‐down control on plants, which in turn influence most ecological processes. Accordingly, the decline, displacement, or extinction of wild large herbivores in African savannas is expected to alter the physical structure of vegetation, the diversity of plant communities, and downstream ecosystem functions. However, herbivore impacts on vegetation comprise both direct and indirect effects and often depend on herbivore body size and plant type. Understanding how herbivores affect savanna vegetation requires disaggregating the effects of different herbivores and the responses of different plants, as well as accounting for both the structural complexity and composition of plant assemblages. We combined high‐resolution Light Detection and Ranging (LiDAR) with field measurements from size‐selective herbivore exclosures in Kenya to determine how herbivores affect the diversity and physical structure of vegetation, how these impacts vary with body size and plant type, and whether there are predictable associations between plant diversity and structural complexity. Herbivores generally reduced the diversity and abundance of both overstory and understory plants, though the magnitude of these impacts varied substantially as a function of body size and plant type: only megaherbivores (elephants and giraffes) affected tree cover, whereas medium‐ and small‐bodied herbivores had stronger effects on herbaceous diversity and abundance. We also found evidence that herbivores altered the strength and direction of interactions between trees and herbaceous plants, with signatures of facilitation in the presence of herbivores and of competition in their absence. While megaherbivores uniquely affected tree structure, medium‐ and small‐bodied species had stronger (and complementary) effects on metrics of herbaceous vegetation structure. Plant structural responses to herbivore exclusion were species‐specific: of five dominant tree species, just three exhibited significant individual morphological variation across exclosure treatments, and the size class of herbivores responsible for these effects varied across species. Irrespective of exclosure treatment, more species‐rich plant communities were more structurally complex. We conclude that the diversity and architecture of savanna vegetation depend on consumptive and nonconsumptive plant–herbivore interactions; the roles of herbivore diversity, body size, and plant traits in mediating those interactions; and a positive feedback between plant diversity and structural complexity.