The presence of white matter lesions in patients with cerebral small vessel disease (SVD) is among the main causes of cognitive decline. We investigated the relation between white matter hyperintensity (WMH) locations and executive and language abilities in 442 SVD patients without dementia with varying burden of WMH. We used Stroop Word Reading, Stroop Color Naming, Stroop Color-Word Naming, and Category Fluency as language measures with varying degrees of executive demands. The Symbol Digit Modalities Test (SDMT) was used as a control task, as it measures processing speed without requiring language use or verbal output. A voxel-based lesion-symptom mapping (VLSM) approach was used, corrected for age, sex, education, and lesion volume. VLSM analyses revealed statistically significant clusters for tests requiring language use, but not for SDMT. Worse scores on all tests were associated with WMH in forceps minor, thalamic radiations and caudate nuclei. In conclusion, an association was found between WMH in a core frontostriatal network and executive-verbal abilities in SVD, independent of lesion volume and processing speed. This circuitry underlying executive-language functioning might be of potential clinical importance for elderly with SVD. More detailed language testing is required in future research to elucidate the nature of language production difficulties in SVD.