Understanding the generation of damaging, high‐frequency ground motions during earthquakes is essential both for fundamental science and for effective hazard preparation. Various theories exist regarding the origin of high‐frequency ground motions, including the standard paradigm linked to slip heterogeneity on the rupture plane, and alternative perspectives associated with fault complexity. To assess these competing hypotheses, we measure ground motion amplitudes in different frequency bands for 3 ≤ M ≤ 5.8 earthquakes in Southern California and compare them to empirical ground motion models. We utilize a Bayesian inference technique called the Integrated Nested Laplace Approximation (INLA) to identify earthquake source regions that produce higher or lower ground motions than expected. Our analysis reveals a strong correlation between fault complexity measurements and the high‐frequency ground motion event terms identified by INLA. These findings suggest that earthquakes on complex faults (or fault networks) lead to stronger‐than‐expected ground motions at high frequencies. Plain Language Summary An important and unresolved question in earthquake science is how damaging, rapid ground shaking is generated during an earthquake. Various ideas currently exist to explain the cause of such ground motions, with the standard view attributing strong ground motion to frictional variations on the fault plane that ruptures during an earthquake. However, recent studies have also indicated that geometric complexities within fault networks may likewise influence the strong ground shaking. To help resolve this conundrum, we analyzed the ground motions produced by earthquakes in Southern California to assess the dependence of these ground motions to the complex fault networks on which the earthquakes occur. Our findings indicate that complex fault network systems have a substantial influence on how damaging earthquake ground shaking could be. These results have broad implications for our understanding of the physics of earthquakes and have important implications for earthquake hazards. Key Points We investigate the influence of fault network complexity on the high‐frequency ground motions of earthquakes in California We observe a strong correlation between fault complexity and residual ground motions at high frequencies The correlation is frequency‐dependent, with stronger correlations observed at frequencies above 2 Hz