Following the quest for new composite materials for bone tissue engineering, a novel elastic hydroxyapatite–glucan composite loaded with two aminoglycoside antibiotics was prepared. The porosity of the composite and the drug release profiles in closed-loop and semi-open systems were tested. The antibacterial activity of the drug was estimated against two Gram-positive and two Gram-negative bacterial strains causing orthopedic infections. It was found that the loaded antibiotic acted in a biphasic mode. The majority of the drug was released within 48–119 h in a pore-dependent manner and inhibited the bacterial growth in the culture medium. However, a small residual amount of the drug was bound to the composite microstructure via ionic interactions and acted as a short-lived barrier against bacterial adhesion to the composite, although the surrounding medium was no longer protected against bacterial infection. Sub-inhibitory concentrations of the released drug were observed in the medium only during the last two days of the experiment (minimized risk of occurrence of drug-resistant strains). Thus the novel drug-loaded elastic hydroxyapatite–glucan composite, demonstrating a biphasic mode of antibacterial action, may be recommended for antibiotic prophylaxis in bone substitute implantation, with less emphasis on the treatment of bone infections.