Low-density polyethylene is one of the basic polymers used in medicine for a variety of purposes; so, the relevant improvements in functional properties are discussed here, making it safer to use as devices or implants during surgery or injury. The objective of the laboratory-prepared material was to study the antimicrobial and biocompatible properties of low-density polyethylene composites with 3 wt. % hybrid nanoclay filler. We found that the antimicrobial activity was mainly related to the filler, i.e., the hybrid type, where inorganic clay minerals, vermiculite or montmorillonite, were intercalated with organic chlorhexidine diacetate and subsequently decorated with Ca-deficient hydroxyapatite. After fusion of the hybrid nanofiller with polyethylene, intense exfoliation of the clay layers occurred. This phenomenon was confirmed by the analysis of the X-ray diffraction patterns of the composite, where the original basal peak of the clays decreased or completely disappeared, and the optimal distribution of the filler was observed using the transmission mode of light microscopy. Functional property testing showed that the composites have good antibacterial activity against Staphylococcus aureus, and the biocompatibility prediction demonstrated the formation of Ca- and P-containing particles through an in vitro experiment, thus applicable for medical use.