The efficiency of delivering a therapeutic agent into a tumor is among the crucial factors determining the prospects for its clinical use. This problem is particularly acute in the case of targeted antitumor agents since many of them are high-molecular-weight compounds. In this work, the penetration of therapeutic agents of two distinct molecular weights into the spheroids of ovarian adenocarcinoma overexpressing human epidermal growth factor receptor 2 (HER2) was studied. It was shown that the low-molecular-weight chemotherapy drug, doxorubicin (~0.5 kDa), effectively penetrates through almost the entire depth of a 300 to 400 μm spheroid, while the penetration depth of the HER2-specific recombinant targeted toxin, DARPin-LoPE (~42 kDa), is only a few surface layers of cells and does not exceed 70 μm. The low penetration of the targeted toxin into spheroid was shown along with a significant decrease in its efficiency against the three-dimensional tumor spheroid as compared with the two-dimensional monolayer culture. The approaches to increasing the accumulation of agents in the tumor are presented and prospects of their use in order to improve the effectiveness of therapy are discussed.