Sound symbolism, the surprising semantic relationship between meaningless pseudowords (e.g., `maluma', `takete') and abstract (round vs. sharp) shapes, is a hitherto unexplained human-specific knowledge domain. Here we explore whether abstract sound symbolic links can be explained by those between the sounds and shapes of bodily actions. To this end, we asked human subjects to match pseudowords with abstract shapes and, in a different experimental block, the sounds of actions with the shapes of the trajectories of the actions causing these same sounds. Crucially, both conditions were also crossed. Our findings reveal concordant matching in the sound symbolic and action domains, and, importantly, significant correlations between them. We conclude that the sound symbolic knowledge interlinking speech sounds and abstract shapes is explained by audiovisual information immanent to action experience along with acoustic similarities between speech and action sounds. These results demonstrate a fundamental role of action knowledge for abstract sound symbolism, which may have been key to human symbol-manipulation ability.