Seed coating ensures the targeted delivery of various compounds from the early stages of development to increase crop quality and yield. Silicon and alginate are known to have plant biostimulant effects. Rice husk (RH) is a significant source of biosilica. In this study, we coated mung bean seeds with an alginate–glycerol–sorbitol (AGS) film with embedded biogenic nanosilica (SiNPs) from RH, with significant plant biostimulant activity. After dilute acid hydrolysis of ground RH in a temperature-controlled hermetic reactor, the resulting RH substrate was neutralized and calcined at 650°C. The structural and compositional characteristics of the native RH, the intermediate substrate, and SiNPs, as well as the release of soluble Si from SiNPs, were investigated. The film for seed coating was optimized using a mixture design with three factors. The physiological properties were assessed in the absence and the presence of 50 mM salt added from the beginning. The main parameters investigated were the growth, development, metabolic activity, reactive oxygen species (ROS) metabolism, and the Si content of seedlings. The results evidenced a homogeneous AGS film formation embedding 50-nm amorphous SiNPs having Si–O–Si and Si–OH bonds, 0.347 cm3/g CPV (cumulative pore volume), and 240 m2/g SSA (specific surface area). The coating film has remarkable properties of enhancing the metabolic, proton pump activities and ROS scavenging of mung seedlings under salt stress. The study shows that the RH biogenic SiNPs can be efficiently applied, together with the optimized, beneficial alginate-based film, as plant biostimulants that alleviate saline stress from the first stages of plant development.