Primary Sjögren’s syndrome (pSS) can be associated with neurological and cognitive involvement, negatively affecting patients’ quality of life. The aim of this study was to assess whether pSS patients are at higher risk of hospitalization for neurological diseases. Through a nationwide retrospective study using the French Health insurance database (based on International Classification for Disease codes, ICD-10), we selected patients hospitalized with new-onset pSS between 2011 and 2018. We compared the incidence of hospitalization for dementia, multiple sclerosis (MS), encephalitis, and peripheral neuropathy with an age- and sex-matched (1:10) hospitalized control group. Adjusted Hazard Ratios (aHR) considered confounding factors, particularly socio-economic status and cardiovascular diseases. We analyzed 25,661 patients hospitalized for pSS, compared with 252,543 matched patients. The incidence of hospitalization for dementia was significantly higher in pSS patients (aHR = 1.27 (1.04–1.55); p = 0.018), as well as the incidence of hospitalization for MS, encephalitis, and inflammatory polyneuropathies (aHR = 3.66 (2.35–5.68), p < 0.001; aHR = 2.66 (1.22–5.80), p = 0.014; and aHR = 23.2 (12.2–44.5), p < 0.001, respectively). According to ICD-10 codes, pSS patients exhibited a higher incidence of hospitalization for dementia, encephalitis, MS, and peripheral neuropathies than controls. Physicians must be aware of these neurological risks to choose the most appropriate diagnostic work-up.