Beneficial features of biocompatible high-capacity UiO-66 nanoparticles, mesoporous SiO₂, and folate-conjugated pluronic F127 were combined to prepare the core–shell UiO-66@SiO₂/F127-FA drug delivery carrier for targeted cellular uptake in cancer treatment. UiO-66 and UiO-66-NH₂ nanoparticles with a narrow size and shape distribution were used to form a series of core–shell MOF@SiO₂ structures. The duration of silanization was varied to change the thickness of the SiO₂ shell, revealing a nonlinear dependence that was attributed to silicon penetration into the porous MOF structure. Doxorubicin encapsulation showed a similar final loading of 5.6 wt % for both uncoated and silica-coated particles, demonstrating the potential of the nanocomposite’s application in small molecule delivery. Silica coating improved the colloidal stability of the composites in a number of model physiological media, enabled grafting of target molecules to the surface, and prevented an uncontrolled release of their cargo, with the drawback of decreased overall porosity. Further modification of the particles with the conjugate of pluronic and folic acid was performed to improve the biocompatibility, prolong the blood circulation time, and target the encapsulated drug to the folate-expressing cancer cells. The final DOX-loaded UiO-66@SiO₂/F127-FA nanoparticles were subjected to properties characterization and in vitro evaluation, including studies of internalization into cells and antitumor activity. Two cell lines were used: MCF-7 breast cancer cells, which have overexpressed folate receptors on the cell membranes, and RAW 264.7 macrophages without folate overexpression. These findings will provide a potential delivery system for DOX and increase the practical value of MOFs.