While structural network analysis consolidated the hypothesis of cerebral small vessel disease (SVD) being a disconnection syndrome, little is known about functional changes on the level of brain networks. In patients with genetically defined SVD (CADASIL, n = 41) and sporadic SVD (n = 46), we independently tested the hypothesis that functional networks change with SVD burden and mediate the effect of disease burden on cognitive performance, in particular slowing of processing speed. We further determined test–retest reliability of functional network measures in sporadic SVD patients participating in a high‐frequency (monthly) serial imaging study (RUN DMC—InTENse, median: 8 MRIs per participant). Functional networks for the whole brain and major subsystems (i.e., default mode network, DMN; fronto‐parietal task control network, FPCN; visual network, VN; hand somatosensory‐motor network, HSMN) were constructed based on resting‐state multi‐band functional MRI. In CADASIL, global efficiency (a graph metric capturing network integration) of the DMN was lower in patients with high disease burden (standardized beta = −.44; p [corrected] = .035) and mediated the negative effect of disease burden on processing speed (indirect path: std. beta = −.20, p = .047; direct path: std. beta = −.19, p = .25; total effect: std. beta = −.39, p = .02). The corresponding analyses in sporadic SVD showed no effect. Intraclass correlations in the high‐frequency serial MRI dataset of the sporadic SVD patients revealed poor test–retest reliability and analysis of individual variability suggested an influence of age, but not disease burden, on global efficiency. In conclusion, our results suggest that changes in functional connectivity networks mediate the effect of SVD‐related brain damage on cognitive deficits. However, limited reliability of functional network measures, possibly due to age‐related comorbidities, impedes the analysis in elderly SVD patients.