Optimal allocation of ward beds is crucial given the respiratory nature of COVID-19, which necessitates urgent hospitalization for certain patients. Several governments have leveraged technology to mitigate the pandemic’s adverse impacts. Based on clinical and demographic variables assessed upon admission, this study predicts the length of stay (LOS) for COVID-19 patients in hospitals. The Kolmogorov–Gabor polynomial (a.k.a., Volterra functional series) was trained using regularized least squares and validated on a dataset of 1600 COVID-19 patients admitted to Khorshid Hospital in the central province of Iran, and the five-fold internal cross-validated results were presented. The Volterra method provides flexibility, interactions among variables, and robustness. The most important features of the LOS prediction system were inflammatory markers, bicarbonate (HCO3), and fever—the adj. R2 and Concordance Correlation Coefficients were 0.81 [95% CI: 0.79–0.84] and 0.94 [0.93–0.95], respectively. The estimation bias was not statistically significant (p-value = 0.777; paired-sample t-test). The system was further analyzed to predict “normal” LOS = 7 days versus “prolonged” LOS > 7 days groups. It showed excellent balanced diagnostic accuracy and agreement rate. However, temporal and spatial validation must be considered to generalize the model. This contribution is hoped to pave the way for hospitals and healthcare providers to manage their resources better.