Background and Objectives: Patients with primary Sjögren’s disease (pSjD) show contradictory results regarding the activity of the hypothalamic–pituitary–adrenal (HPA) axis. The aim of this study was to determine the salivary cortisol concentration to evaluate the function of the HPA axis (hypoactive/hyperactive) between patients with pSjD and control subjects. Materials and Methods: A total of 34 subjects participated in the cross-sectional study: 17 patients with pSjD and 17 control subjects. Stimulated whole saliva (SWS) was used to determine salivary cortisol concentration using an enzyme-linked immunosorbent assay (ELISA). Results: The salivary cortisol concentration showed a statistically significant difference between patients with pSjD and control subjects (4.69 ± 2.88 vs. 0.49 ± 0.37; p < 0.001; Student t-test). The area under the curve (AUC) was 100.0% in patients with pSjD (p < 0.001). The cut-off point was set to >1.454. The patients with pSjD had four times higher scores for depression and stress and six times higher scores for anxiety compared to the control subjects (p = 0.048, p < 0.001, p = 0.038; Mann–Whitney U test). The patients with pSjD had a statistically significantly higher total Oral Health Impact Profile (OHIP) score compared to the control subjects (p < 0.001, Mann–Whitney U test). Conclusions: The patients with pSjD showed short-term hyperactivity of the HPA axis compared to the control subjects.