Abstract Species introductions can alter local food‐web structure by changing the vertical or horizontal diversity within communities, largely driven by their body size distributions. Increasing vertical and horizontal diversities is predicted to have opposing effects on stability. However, their interactive effects remain largely overlooked. We investigated the independent and collective effects of vertical and horizontal diversities on food‐web stability in alpine lakes stocked with variable body size distributions of introduced fish species. Introduced predators destabilize food‐webs by increasing vertical diversity through food chain lengthening. Alternatively, increasing horizontal diversity results in more stable food‐web topologies. A non‐linear interaction between vertical and horizontal diversities suggests that increasing vertical diversity is most destabilizing when horizontal diversity is low. Our findings suggest that the size structure of introduced predators drives their impacts on stability by modifying the structure of food‐webs, and highlights the interactive effects of vertical and horizontal diversities on stability.