Nowadays, the use of statistical approaches, i.e., Box–Bhenken designs, are becoming very effective for developing and optimizing pharmaceutical drug formulations. In the current work, a Box–Bhenken design was employed using Design Expert version 11 to develop, evaluate, and optimize a hydrogel-based formulation for sustained release of an antiviral drug, i.e., favipiravir. The hydrogels were prepared using the free radical polymerization technique. β-Cyclodextrin (β-CD), N,N′-methylenebisacrylamide (MBA), acrylic acid (AA), and potassium per sulfate (KPS) were used as oligomer, crosslinker, monomer, and initiator, respectively. Three variables, including β-CD (X1), MBA (X2), and AA (X3) were used at various concentrations for the preparation of hydrogels, followed by evaluation of a sol–gel fraction, swelling, porosity, chemical compatibilities, in vitro drug release, and entrapment efficiency. The results of the studies revealed that the degree of swelling was pH dependent, the best swelling being at pH 7.2 (1976%). On the other hand, for the low sol fraction of 0.2%, the reasonable porosity made the hydrogel capable of loading 99% favipiravir, despite its hydrophobic nature. The maximum entrapment efficiency (99%) was observed in optimized hydrogel formulation (F15). Similarly, in vitro drug release studies showed that the prepared hydrogels exhibited a good, sustained release effect till the 24th hour. The kinetic modelling of drug release data revealed that the Korsmeyer–Peppas model was best fit model, describing a diffusion type of drug release from the prepared hydrogels. Conclusively, the outcomes predict that the hydrogel-based system could be a good choice for developing a sustained-release, once-daily dosage form of favipiravir for improved patient compliance.