Background/Objectives: Individuals with post-COVID-19 conditions risk developing short- and/or long-term neuromuscular impairments, including postural imbalance. However, there is limited evidence showing whether balance deficits are associated with declines in the functional status in post-COVID-19 individuals. This study examined postural balance in non-hospitalized post-COVID-19 individuals using different assessment tools and tested the most relevant balance tools in predicting functional status. Methods: This cross-sectional study enrolled 60 adults split into control (n = 30) and post-COVID-19 (n = 30) groups. Postural balance was assessed in both groups using the Functional Reach Test (FRT), Berg Balance Scale (BBS), Timed Up and Go (TUG), Tinetti Balance Test (Tinetti), and Mini-BESTest (MBT). Functional status in the post-COVID-19 group was assessed using post-COVID-19 functional status (PCFS). Results: Significant differences in postural stability between groups were found only for the FRT. All balance tests showed a statistically significant correlation with PCFS in the post-COVID-19 group, with better performance in all tests being associated with better functional status: Tinetti (r = −0.584), FRT (r = −0.542), MBT (r = −0.530), BBS (r = −0.415) and TUG (r = 0.368). Tinetti was the independent variable that significantly played an important role in determining PCFS (adjusted R2 = 0.318, p < 0.001). Conclusions: Post-COVID-19 functional status is best determined by the Tinetti Balance Test, making it an effective tool for assessing postural balance deficits in this population, with potential implications for postural control assessment and rehabilitation.