Three porous matrices based on poly(lactic acid) are proposed herein for the controlled release of amikacin. The materials were fabricated by the method of spraying a surface liquid. Description is given as to the possibility of employing a modifier, such as a silica nanocarrier, for prolonging the release of amikacin, in addition to using chitosan to improve the properties of the materials, e.g., stability and sorption capacity. Depending on their actual composition, the materials exhibited varied efficacy for drug loading, as follows: 25.4 ± 2.2 μg/mg (matrices with 0.05% w/v of chitosan), 93 ± 13 μg/mg (with 0.08% w/v SiO2 amikacin modified nanoparticles), and 96 ± 34 μg/mg (matrices without functional additives). An in vitro study confirmed extended release of the drug (amikacin, over 60 days), carried out in accordance with the mathematical Kosmyer–Pepas model for all the materials tested. The matrices were also evaluated for their effectiveness in inhibiting the growth of bacteria such as Staphylococcus aureus, Escherichia coli, Klebsiella pneumoniae, and Pseudomonas aeruginosa. Concurrent research was conducted on the transdermal absorption, morphology, elemental composition, and thermogravimetric properties of the released drug.