Human tissue lacks a defense mechanism against cancer cells and their rapid replication. One of the primary ways to combat such malignant abnormalities is through direct removal of the resulting cancer tissue, application of chemotherapy (antitumor drugs), or radiation. Doxorubicin (DOX), a chemotherapeutic drug, and its bioactive derivatives are among the most widespread drugs for such treatments. The development of less invasive, “smart” materials, such as drug delivery systems, arose from the need for advanced tumor treatment methods. Targeted drug delivery ensures localized treatment of tumor tissue, minimizing exposure to the entire body. Chitosan (CHT) is known for its biocompatibility, hydrophilicity, non-toxicity, and biodegradability. Moreover, chitosan has a polycationic nature due to the presence of amino groups, which allows drug release from polymeric matrices depending on the pH value of the medium, ensuring intracellular delivery of antitumor drugs. This study investigates the impact of different incubation media on the release profile of the antitumor drug (doxorubicin) from prepared composite materials based on hydroxyapatite and chitosan physically cross-linked with copper (II) ions (CHT-Cu/CaP), using fluorescence spectrophotometry. The release of DOX from microparticles of different chemical compositions (0, 5, and 10 wt.% CaP) was monitored over 72 hours in phosphate buffer solution at pH 6 (PB-6) and 7.4 (PB-7.4), as well as in cell culture medium (CCM). The results indicate greater drug release from microparticles with the highest amount of the inorganic phase (CHT-Cu/CaP10), while the smallest amount of DOX was released from microparticles without CaP (CHT-Cu/CaP0). The medium in which the largest amount of doxorubicin was released is cell culture medium (CCM), followed by PB-6 and then PB-7,4. Such results are attributed to the stability of the microcarriers due to the stability of calcium phosphate and limited solubility of chitosan under physiological conditions. The obtained results indicate that the chemical composition of microcarriers, as well as composition and pH value of the incubation medium influence the drug release profile, and suggest that CHT-Cu/CaP microcarriers have immense potential for use as doxorubicin delivery systems for targeted drug delivery in bone cancer treatment.