Nowadays, the demand for food packaging that maintains the safety and quality of products has become one of the leading challenges. It can be solved by developing functional materials based on biodegradable polymers, such as poly(lactic acid) (PLA). In order to develop PLA-based functional materials with antibacterial activity, silver nanoparticles (AgNPs) were introduced. In the present study, AgNPs stabilized by a copolymer of ethylene and maleic acid were used. Under the joint action of shear deformations and high temperature, the biocomposites of PLA with poly(ethylene glycol) and AgNPs were produced. Their mechanical and thermal characteristics, water absorption, and structure were investigated using modern methods (DSC, FTIR, Raman spectroscopy, SEM). The effect of AgNP concentration on the characteristics of PLA-based biocomposites was detected. Based on the results of antibacterial activity tests (against Gram-positive and Gram-negative bacteria, along with yeast) it is assumed that these systems have potential as materials for extending the storage of food products. At the same time, PLA–PEG biocomposites with AgNPs possess biodegradability.