The current research work focuses on the extraction and optimization of the hydrogel (AVM) from the seeds of Artemisia vulgaris using Box–Behnken design-response surface methodology (BBD-RSM). The AVM was obtained through a hot water extraction process. The influence of different factors, including pH (U = 4 to 10), temperature (V = 25 to 110 °C), seed/water ratio, i.e., S/W ratio (W = 1/10 to 1/70 w/v), and seed/water contact time, i.e., S/W time (X = 1 to 12 h) on the yield of AVM was evaluated. The p-value for the analysis of variance (ANOVA) was found to be <0.001, indicating that the yield of AVM mainly depended on the abovementioned factors. The highest yield of AVM, i.e., 15.86%, was found at a pH of 7.12, temperature of 80.04 °C, S/W ratio of 1/33.24 w/v, and S/W time of 8.73 h according to Design-Expert Software. The study of the pH-responsive behavior of AVM in tablet form (formulation AVT3) revealed that AVM is a pH-responsive material with significantly high swelling at pH 7.4. However, less swelling was witnessed at pH 1.2. Moreover, AVM was found to be a sustained release material for esomeprazole at pH 7.4 for 12 h. The drug release from AVT3 was according to the super case-II transport mechanism and zero-order kinetics.