Chitosan exhibits unique properties making it a suitable material for drug delivery. Considering the rising popularity of hydrogels in this field, this work offers a comprehensive study of hydrogels constituted by chitosan and cross-linked with 1,3,5-benzene tricarboxylic acid (BTC; also known as trimesic acid). Hydrogels were prepared by cross-linking chitosan with BTC in different concentrations. The nature of the gels was studied through oscillatory amplitude strain and frequency sweep tests within the linear viscoelastic region (LVE) limit. The flow curves of the gels revealed shear thinning behavior. High G′ values imply strong cross-linking with improved stability. The rheological tests revealed that the strength of the hydrogel network increased with the cross-linking degree. Hardness, cohesiveness, adhesiveness, compressibility, and elasticity of the gels were determined using a texture analyzer. The scanning electron microscopy (SEM) data of the cross-linked hydrogels showed distinctive pores with a pore size increasing according to increasing concentrations (pore size range between 3–18 µm). Computational analysis was performed by docking simulations between chitosan and BTC. Drug release studies employing 5-fluorouracil (5-FU) yielded a more sustained release profile with 35 to 50% release among the formulations studied in a 3 h period. Overall, this work demonstrated that the presence of BTC as cross-linker leads to satisfactory mechanical properties of the chitosan hydrogel, suggesting potential applications in the sustained release of cancer therapeutics.