The properties of sodium hyaluronate (HA), such as hygroscopicity, flexibility, the ability to form hydrogels, as well as biocompatibility and biodegradability, are beneficial for the applications in pharmaceutical technology, cosmetics industry, and aesthetic medicine. The aim of this study was to prepare HA-based hydrogels doped with active pharmaceutical ingredient (API): a cationic drug—lidocaine hydrochloride or anionic drug—sodium. The interaction between the carrier and the implemented active pharmaceutical substances was evaluated in prepared systems by applying viscometric measurements, performing release tests of the drug from the obtained formulations, and carrying out FTIR and DSC. The data from release studies were analyzed using the zero-, first-, and second-order kinetics and Higuchi, Korsmeyer-Peppas, and Hixon-Crowell models. The respective kinetic parameters: the release rate constants, the half-release time and, in the case of the Korsmeyer-Peppas equation, the n parameter were calculated. The variability between the obtained release profiles was studied by calculating the difference (f1) and the similarity factor (f2) as well as employing statistical methods. It was revealed that the incorporation of the drugs resulted in an increase in the viscosity of the hydrogels in comparison to the respective drug-free preparations. The dissolution study showed that not entire amount of the added drug was released from the formulation, suggesting an interaction between the carrier and the drug. The FTIR and DSC studies confirmed the bond formation between HA and both medicinal substances.