The ability to control balance and prevent falls while carrying out daily life activities may require a predominantly controlled (cognitive) or automatic processing depending on the balance challenge, age, or other factors. Consequently, this process may be affected by mental fatigue which has been shown to impair cognitive abilities. Controlling static balance in young adults is a relatively easy task that may proceed automatically with minimal cognitive input making it insusceptible to mental fatigue. To investigate this hypothesis, static single and dual task (while concurrently counting backward by seven) balance was assessed in 60 young adults (25.2 ± 2.4 years) before and after 45 min of Stroop task (mental fatigue condition) and watching documentary (control), presented in a randomized counterbalanced order on separate days. Moreover, because mental fatigue can occur due to task underload or overload, participants carried out two different Stroop tasks (i.e., all congruent, and mainly incongruent trials) on separate days in the mental fatigue condition. Results of the study revealed a significantly higher feeling of mental fatigue after the mental fatigue conditions compared to control (p < 0.001). Similarly, the performance on congruent Stroop trials decreases with time indicating objective mental fatigue (p < 0.01). However, there was no difference in balance or concurrent task performance under both single and dual task assessments between the three conditions (p > 0.05) indicating lack of effect of mental fatigue on static balance in this population. Therefore, future studies investigating this phenomenon in occupational or sport settings in similar population should consider using more challenging balance tasks.