The creation of antibacterial nanocomposites that provide prolonged release of encapsulated drugs is of great interest for various fields of medicine (dentistry, tissue regeneration, etc.). This article demonstrates the possibility of creating such nanocomposites based on sodium alginate and drug-templated mesoporous silica nanocontainers (MSNs) loaded with two bioactive substances. Herein, we thoroughly study all stages of the process, starting with the synthesis of MSNs using antiseptic micelles containing the hydrophobic drug quercetin and ending with assessing the activity of the resulting composites against various microorganisms. The main emphasis is on studying the quercetin solubilization in antiseptic micelles as well as establishing the relationship between the conditions of MSN synthesis and micelle morphology and capacity. The effect of medium pH on the release rate of encapsulated drugs is also evaluated. It was shown that the MSNs contained large amounts of encapsulated drugs and that the rate of drug unloading depended on the medium pH. The incorporation of such MSNs into the alginate matrix allowed for a prolonged release of the drugs.