L-asparaginase (ASNase) is an amidohydrolase that can be used as a biopharmaceutical, as an agent for acrylamide reduction, and as an active molecule for L-asparagine detection. However, its free form displays some limitations, such as the enzyme’s single use and low stability. Hence, immobilization is one of the most effective tools for enzyme recovery and reuse. Silica is a promising material due to its low-cost, biological compatibility, and tunable physicochemical characteristics if properly functionalized. Ionic liquids (ILs) are designer compounds that allow the tailoring of their physicochemical properties for a given task. If properly designed, bioconjugates combine the features of the selected ILs with those of the support used, enabling the simple recovery and reuse of the enzyme. In this work, silica-based supported ionic liquid-like phase (SSILLP) materials with quaternary ammoniums and chloride as the counterion were studied as novel supports for ASNase immobilization since it has been reported that ammonium ILs have beneficial effects on enzyme stability. SSILLP materials were characterized by elemental analysis and zeta potential. The immobilization process was studied and the pH effect, enzyme/support ratio, and contact time were optimized regarding the ASNase enzymatic activity. ASNase–SSILLP bioconjugates were characterized by ATR-FTIR. The bioconjugates displayed promising potential since [Si][N3444]Cl, [Si][N3666]Cl, and [Si][N3888]Cl recovered more than 92% of the initial ASNase activity under the optimized immobilization conditions (pH 8, 6 × 10−3 mg of ASNase per mg of SSILLP material, and 60 min). The ASNase–SSILLP bioconjugates showed more enhanced enzyme reuse than reported for other materials and immobilization methods, allowing five cycles of reaction while keeping more than 75% of the initial immobilized ASNase activity. According to molecular docking studies, the main interactions established between ASNase and SSILLP materials correspond to hydrophobic interactions. Overall, it is here demonstrated that SSILLP materials are efficient supports for ASNase, paving the way for their use in the pharmaceutical and food industries.